Vaan headcanon! Will be added to as I think of more things. (It's entirely possible these may contradict info in like, the Ultimania guide)
Vaan was actually not born in Rabanastre. His parents were from a village miles up the Nebra, and once they knew they were going to have a second child, they took Reks and made their way to the capital. They had been to Rabanastre once before, and wanted their next son to live in what they felt was a truly wonderful city. It was apparent after a week of travel that Vaan's mother couldn't handle the rest of the trip, so they stayed in one of the outposts for a few months to have Vaan. She was very sick up through the birthing process and Vaan's father was afraid she would die, but he was also somewhat resigned to it. She survived, and the whole village threw a celebration in honor of her and her new son.
The plague that struck most of Dalmasca took 5,000 people with it, many of them centered in the capital. There were public mourning ceremonies almost every week. It was the first time Vaan became aware of the presence of death, and he sometimes recalls seeing the people in the streets dressed all in black. He remembers thinking that the departure from their brightly-colored clothes and their smiles and laughter was fundamentally wrong, and he was afraid.
Vaan's parents died when he was five and a half. He knew they were going to die days before they actually did, but he still cried for two days, "one day for each of them," he would later admit. Penelo's family took him in at this time, but her parents only lived for another few years before succumbing to the plague, as well. Her older brothers kept watch then, but they let Reks and Vaan live in their own apartment in Lowtown as long as they kept it clean.
Reks was gay. This doesn't really have any bearing on Vaan, as Reks never told him (and was very good at keeping it under wraps) but it's headcanon anyway, so.
The first time Vaan saw Old Dalan, he was almost seven; he thought Dalan was an evil spirit and threw a rock at his head and ran screaming through Lowtown. Reks scolded him very hard, and made Vaan apologize, which he did, sheepishly. The bruise did not go away for weeks, and Dalan eventually admitted that the boy had a good arm. This made Vaan feel very proud.
Some of the local boys used to tease Penelo. Vaan would tell them to stop because she would hurt them if they made her too mad, but they didn't listen until she kicked them in the shins. Vaan knew how hard she could kick from first-hand experience. (He used to tease her when he first moved in with her family; it didn't last long.)
During Vaan's childhood and adolescence, there were three things that street kids were taught if they wanted to survive: how to pickpocket, how to be a street ear, and how to lie convincingly. Vaan was good at the first two things, and decent at the third. (He can never lie to Penelo no matter how hard he tries.)
No matter how Vaan's relationship with Penelo progresses, he will always think of her as his partner in everything.
Dalmascan culture lends itself well to music and dance. Vaan can't sing, nor can he dance too well, but he can play the drums. He likes to whistle when he's daydreaming, sometimes. It annoyed Balthier to no end during their travels.
On the subject of Balthier, Vaan will act annoyed when people insinuate that he's Balthier's apprentice, but he's not actually that bothered by it. He thinks Balthier is arrogant and patronizing and he's pretty sure Balthier likes to speak extra-complicated when Vaan's around just to make him look stupid, but deep inside Vaan does look up to Balthier.
Vaan still thinks it's really cool that he and Ashe are friends. He really cares about her, and did at one point have a puppy crush on her, but it's mostly faded by now. To Vaan, meeting and getting to know Ashe was like living proof that Dalmasca wasn't completely crushed by the Empire, that there was still hope, that Dalmasca could fight back and that there was still a chance to make things right. Vaan wanted to do everything he could to help Ashe achieve this goal.
At the same time, he knows she's not perfect. He's aware that he isn't, either, but he also knows the greatest thing that helps him get through when his flaws try to stand in the way, and that's his friends. Vaan tries to be a good friend to Ashe.
Vaan will probably never not be a little bit intimidated by Fran. He also makes a conscious effort to keep his eyes above her neck at all times. It hurts his neck a lot.
Vaan's thoughts on Larsa are somewhat complicated. During their first few encounters, Vaan didn't like Larsa that much. He thought he was snooty and condescending, and when Larsa rescued Penelo from Ghis outside Lhusu, Vaan would've ran out from the mines to try and stop them if Fran hadn't said he was trustworthy. Learning that Larsa was an Imperial only added to his distrust. Once reuniting with Penelo on Leviathan, however, Vaan started to see Larsa in a different light. Though this wasn't enough to stop him from being snide to Larsa in calling him by his pseudonym. Afterward, however, he felt kind of ashamed of himself, because it was clear that Larsa had taken good care of Penelo, and might even be different from other Imperials. From this point on, Vaan starts to take a different perspective on the events going on around him -- he starts to think that there's more to the story than what his experiences tell him. He learns from Penelo what Larsa did for her, and begins to consider him as a potential ally. Meeting up with him in Jahara gives Vaan an opportunity to know Larsa as someone who's not just Archadian, but a person. He discovers that he likes Larsa, that he gets along with Larsa, and that he starts to come to see Larsa as a friend. When Vaan tells Ashe that Larsa's "not bad for an Imperial," he means it in more ways than one. Like Ashe, Larsa is a representation of hope; hope that not all Imperials are evil, that there are those who want peace instead of war, who want to work together. Larsa teaches Vaan to consider some things carefully, and to not judge a book by its cover. Larsa is also connected to Ashe in another way, aside from the fact that they're two of the most powerful political figureheads in Ivalice, and that is their personalities. Vaan gets why he saw Larsa as condescending when they first met: it was because Larsa had a goal in mind and wasn't going to show any hesitation. Vaan thinks that if he were the Emperor of Archadia, he'd probably be a little snooty, too. But he knows Larsa is a good person, so he can let that pass. He recognizes that Larsa's way beyond his years, and so in a way, looks up to him. Larsa might not be the first person Vaan would go to if he was having problems, but that doesn't mean he wouldn't. He'd trust Larsa to listen to him, and to give him perspective.