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By day, Tsuzuki is a mild-mannered, sweet, dumb detective in the NGPD. Generally well-liked despite his frequent tendency to show up to work late and hungover.
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The short answer to this is: Tsuzuki is a darling, lovable MESS.
And now for the long answer.
On the surface, Tsuzuki is the office idiot. A klutz who unintentionally destroys things on a regular basis (as small as a coffee machine or as large as the entire Juuouchou library), he's sweet and cuddly and friendly, so most everyone has a hard time disliking him. He's also a glutton who eats so much so quickly that he tends to get the aim wrong from the fork to his mouth, and he can smell any sweet within the nearest mile. He's a drunk and a lazy slob, who often comes into work late (most of the time slightly hungover), and with his clothes a rumpled mess. He avoids paperwork like the plague, and is content to stay in the backwoods where cases are few and easy instead of doing actual work. If anything, his faults make him more endearing, and everyone likes him as a sort of haphazard pet as well as a good friend. He's far too sensitive. He can't stand to hurt anyone or anything and has no respect for himself. And, apparently, his bouncy, happy, scatterbrain personality covers a huge well of self-hatred and suicidal tendencies.
Tsuzuki desperately wants everyone to think he's simple, one-dimensional. He's not as good as he thinks at keeping up the act, but he sure tries hard. Tsuzuki isn't stupid or lazy; he carries more guilt and remorse than one person should ever have to feel, and he will never get used to the cases that require them to take a human life. He clearly believes that he's worthless, and yet he craves acceptance and love, a dichotomy that drives him to present himself as the office idiot, someone funny and friendly and likable. Even when insulted and pushed away, this need for approval keeps him coming back and never beginning to hate the offender.
But it's not all a front, either. Tsuzuki is genuinely sweet and kind, more than capable of easy, frank affection and he genuinely loves just about everyone he meets. He does like sunny mornings and ice cream and puppies, and he takes joy in little things. He's gentle and patient, and pretty intelligent, but in a casual way that he easily dismisses (and so does everyone else). He's absolutely honest in this one area, if nowhere else: he would never betray a trust, nor hurt a loved one. Tsuzuki always cares, no matter how it hurts him. He's forever doubting and uncertain - especially about himself - and needs unflinching honesty and steadiness since he can't manage it for himself.
Tsuzuki is also very bad at keeping his emotions in check, and often lets them cloud his judgement. He may seem almost frightening and calm when angered, but he comes out with all guns blazing and not much thought for anything else. He does his best to jump in and fix everything for everyone else and try to not let get anyone hurt in the process, but he's so afraid of failure that he often hesitates. He's so sympathetic to others' pain that he loses objectivity and sight of the big picture at times. He also doesn't seem to know the meaning of a "happy medium"; everything he does is all or nothing, extreme and passionate.
Tsuzuki's a hypocrite in weighing his own worth against others; everyone else comes first 99% of the time, but once he loses control of his sanity, he runs to destroy himself without thinking of who he might be hurting in the process. He will always put someone else before himself and throw himself into danger in order to protect someone else, but if someone turns that logic towards him, he blatantly and gently denies it, unable to believe he could be important to anyone and worth saving, ever.
At the time of the series' beginning, Tsuzuki has gotten a lot stronger emotionally since he first started as a shinigami. This is not a positive thing, because he had to grow strong and silent about his emotional ills out of necessity, not out of growth and self-absolving. He realized what a burden he was putting on everyone around him, and rather than bother anyone with his "less than worthy" problems, he simply shut up and closed himself off, rarely leaning on anyone except when cataclysmically vulnerable.
major depression - it's easy to label Tsuzuki as depressed, but he's somewhat asympomatic - he still takes joy in lots of things, especially his hobby of gardening. He's not excessively lethargic, and his horrific work ethic is due to other factors, not apathy or lethargy. However, he does suffer from insufferable guilt and feelings of worthlessness, feels isolated from others, and has trouble with concentration (though that could also be other neuroses). He also possibly sleeps for unnecessarily long periods of time (sleep is described as one of his favorite things and he's often late to work for oversleeping/hangovers). It's also popular fandom opinion that there are just some days where Tsuzuki is in too much despair to get out of bed and just stays there until he can gather the strength to go back out into the world. Much of this is exacerbated by his other conditions. His depression is also underscored by his moral existential anxiety and overwhelming inferiority complex.
borderline personality disorder - One of the common factors to diagnose this condition is a narcissistic view, which Tsuzuki definitely doesn't have. However, having reading several articles, I've decided to keep this condition because it fits him perfectly minus that area, and the narcissism is a tendency and not necessarily an inevitability if one has this condition.
Tsuzuki has rapid mood swings, but they're not severe enough to be considered bipolar. He switches from bouncy/hyper to depressed very easily, and sometimes with little provocation. Many BPD mood swings are punctuated with some sort of aggression, self-harm, or substance abuse - the last two are both definitely Tsuzuki, considering his alcoholism. He's often paranoid about abandonment and hides pieces of himself he thinks are necessary to keep other from hating him, not to mention much too sensitive (easily hurt) and hyper-aware of the reactions of those around him. This is partially because he believes himself to be fundamentally bad and unworthy (another symptom, though it also factors into his other diagnoses).
He has a history of failed relationships of all sorts and none of them could be considered stable during or after the fact. (Tatsumi is the most prominent example of this - he was another partner who was unable to cope with Tsuzuki's extreme instability, and at best the space between them now is tense and awkward.) Tsuzuki often switches between idealizing others and their reactions; when it's different from what he hoped/imagined, he perceives himself to be hated and turns the idealist fantasy completely around. In a typical BPD response, the BPD sufferer would threaten suicide because the reality meant their object of affection didn't care for them. This is another area where Tsuzuki doesn't follow the pattern. BUT it's not impossible to think that being so old and repeating these behaviors for so long, he's become aware that he creates these ideals but is unable to help himself. If anything, he takes it as his own personal failure and hates himself more when his ideals are crumbled. As for a self-disturbed self-image, we don't need to look further than the fact that Tsuzuki can't ascertain for himself whether he's even human or not. Though he's no longer constantly considering or attempting suicide, it's not a far stretch to imagine that he picks at himself (maybe biting the skin of his fingers, nail biting, hair pulling). Need I also mention that depression and alcoholism usually coincide with this condition, as well as impulsive behaviors like binge eating? Oh, and did I mention the dissociation? In canon, Tsuzuki admits that after losing his mind in life, he had periods of lucidity that became less frequent and lasted less time.
So the inverse that he often was "outside himself" in a sense is also true.
As the final nails in the coffin, BPD sufferers usually have a history punctuated by abuse or neglect during childhood (being frequently beaten up by the neighborhood children, and lord knows what else), and then the condition was triggered due to trauma in adolescence to early adulthood (the epic big bad thing that made him lose his mind, anyone?); BPD sufferers are more likely to be victims of violence and rape later in life (Muraki targets Tsuzuki very heavily, and for very twisted reasons?)
post-traumatic stress disorder - it's likely that Tsuzuki buries the memories of whatever trauma he experienced in his past because he simply can't handle the psychological strain. But when confronted with the truth, he usually goes into yet another mental breakdown. After Kyoto, Muraki gets added as a stimulus that Tsuzuki can't mentally handle - when confronted with an illusion of Muraki in the Hall of Candles, Tsuzuki becomes absolutely paralyzed with fear and is unable to speak or move.
attention deficit hyperactive disorder - Tsuzuki has an extremely difficult time keeping focus and fidgets often. He's impulsive and often doesn't think before he acts or speaks. He's extremely disorganized and can't stick to one activity for too long. Not to mention his need to play with something when standing still, and constant fidgeting when sitting.
The biggest problem with Tsuzuki's life-before-death is that not much is known about it. There are clues scattered throughout canon, but still not enough to paint a clear picture. Much is left to the imagination.
Tsuzuki was born in the year 1900, and that's the most solid fact known about his early life. His family is never mentioned, except that he had a sister he loved very much, named Ruka. She's the one who taught him gardening, dancing, and cooking. As a child, he was often physically bullied by his peers for having purple eyes, the mark of demon blood. He never fought back, only running while screaming apologies just for being alive. At age 18, something tragic happened, and Tsuzuki mentally imploded into insanity. Whether he killed someone or many people or just found the demon blood allegations to be true, he couldn't bear it and lost his mind. He spent the next seven years in a hospital, where he continued to live despite being penniless, not to mention not eating, sleeping, or drinking. He attempted suicide countless times, but it seems the shinigami healing ability was one he possessed long before death; his attempts always failed simply because the wounds would heal almost immediately. It wasn't until January 1926 that he finally got "lucky".
Though we don't see the first seventy years of Tsuzuki's "life" as shinigami, we know that he used to be highly unstable and would often fall into horrible depressions if he failed at a job, or should someone innocent die, or any number of triggers. Tsuzuki has been a shinigami so long either because he can't forgive himself and can't move on, OR his crimes were so horrific that his penance hasn't been completed yet. He was never able to keep a partner for longer than two years; his partners often wanted to help Tsuzuki, but in the end could never deal with the depth of his pain.
This was until 1996, when a new shinigami entered the fold. Hisoka Kurosaki was only 16 when he died, and is a fierce opposite to Tsuzuki in many ways. Aloof, misanthropistic, practical, intelligent, and very short-tempered, Hisoka was furious to find he got the shinigami with the department's worst reputation as a partner. Slowly, Hisoka sees a lot of things the others in the office miss - Tsuzuki's work ethic, for one thing, his intelligence and kindness being another. Hisoka grew up without any kindness at all and has a hard time knowing how to react to Tsuzuki, so he tries to push him away. Unfortunately, this ends up getting Hisoka kidnapped. The perpetrator behind their first case together is Muraki, a doctor from Tokyo who mysteriously has many spiritual abilities despite still being alive. Muraki is actually the one who killed Hisoka, and he kidnaps the boy in order to lure Tsuzuki out, knowing that Tsuzuki will run to save Hisoka, even knowing it's a trap. Which is exactly what happens. Tsuzuki and Muraki duke it out with shikigami, but Muraki sends a fatal blow towards a weakened Hisoka - which Tsuzuki takes instead. It shatters his spine, alone with several organs, probably. In desperation, Tsuzuki uses Hisoka's empathy to his advantage and asks if he could channel himself through Hisoka in order to save them both. So they do an epic Vulcan mind meld, and thus are able to escape the burning building more or less alive. Unfortunately, Muraki was also able to. It takes some time, but Hisoka finally decides not to ask for a new partner after this first case of theirs is finished. Tsuzuki selflessly risked his life to save Hisoka from being kidnapped by Muraki, and the boy's never been shown such kindness.
Still, the two are very different and have yet to know their similarities. But they grow and learn through the next two cases they investigate together. Tsuzuki continues to watch out for Hisoka (despite the latter's continued insistence that HE DOESN'T NEED IT and get OFF already) because he likes people and looking after them and he feels (knows?) that Hisoka needs it even if he won't admit it. Besides, even if this partnership ends like so many others, it's best to part on good terms, right? Tsuzuki puts himself out there as Hisoka's support so easily, yet refuses to tell his partner very much about himself. No reason to speed up losing another partner.
The final case in canon is arguably most important. Though it's out of their jurisdiction, Tsuzuki and Hisoka were asked to come to Kyoto for a mysterious and brutal series of serial murders. Muraki is the obvious culprit, but he's proving slippery, and his motives seem to be nothing but breaking Tsuzuki's sanity. Muraki goads Tsuzuki multiple times about the truth behind Tsuzuki's death, and revealing this he has his grandfather's files from when Tsuzuki was alive, and that he had analyzed Tsuzuki's DNA - it isn't human. Muraki uses this information and the deaths innocent bystanders to drive Tsuzuki further into a spiral. And thus he loses his mind. Muraki materializes and steals Tsuzuki away to his lab in order to decapitate him for his own nefarious purposes. Tsuzuki continues to be lost inside his mind, but he does have some moments of lucidity. It was one of those moments where he takes advantage of Muraki's dropped guard - and stabs him. He then recites the incantation to call his shikigami Touda - a black serpent dragon who uses black fire, which is one of the few methods that can guaranteed kill a shinigami. He intends to kill himself, and Muraki with him. By the time Hisoka and the others reach the lab, it's ablaze. Hisoka dives in without thinking because he refuses to let Tsuzuki kill himself. Hisoka finally reaches his partner, but Tsuzuki refuses to be saved. He says that he's tired of living, that he's killed too many people and he shouldn't have existed in the first place (and other such emo things), and Hisoka hugs him. Hisoka's crying, desperate to reach Tsuzuki. He begs Tsuzuki to live, even if the only reason would be to live for Hisoka. Because Hisoka needs him, and all the kindness he gives. Tsuzuki's shocked, but finally relents. They barely escape the inferno alive thanks to Tatsumi, but they've survived together. (Alternatively, in the manga Hisoka says he'd die with Tsuzuki, since his only place is by the other's side. Either way, they make it through.)