Blah blah some headcanon bits for Crowley and all that jazz. Spoilers for Good Omens and um, Supernatural because I can. Yes. Shut up I like my cross-canon shenanigans.
BASICS→ In as he 'Did Not So Much As Fall As Vaguely Sauntered Down', Crowley, in reality, possesses no memories of Heaven whatsoever. The most he recalls is a lot of blue if he tries hard enough, but beyond that he doesn't have an inkling of his time of Above at all, if he had ever been there in the first place. Sometimes Crowley does think on it a little.
→ Due to his lack of memories of Heaven (and thus lacks memories of the Fall), Crowley actually harbours no real hatred for the angels and other holy beings. Sure he fears them, but that's because they can effectively smite him should they wish to. He hates them only because its in his nature to do so - the hate is literally built into him and ingrained into his psyche at the beginning. Of course, time (and Aziraphale) has changed that effectively, but he's still pretty wary about them. Arrangement or not, angels can still smite him pretty badly.
→ Before the Arrangement, there was a good deal of build up to it - he and Aziraphale actually stopped fighting a bit before that year... and well, they weren't really there yet, but by then Crowley knew better than to ask an angel why were they getting each other drunk instead of fighting their asses off like they had been for the last Manchester-knows-when. But hey, things worked out for the most part, so he'd like things to stay that way.
→ As the Serpent of Eden - humanity's first demon, in some senses - Crowley holds within himself a good potential of power. Potential that Crowley isn't very aware of, and has never tapped into because he's never been a fighter in the first place. Flight over fight is always Crowley's choice, but should he ever fight with his original powers... that would be a pretty bad thing for everybody.
→ Being the demon responsible for implanting the original sin into humans, its safe to say that Crowley knows how to make humans tick. Sure, each and everyone of them are different, but he's confident that he'll figure them out eventually. To him, its a bit of a puzzle - one with entertaining rewards as well.
→ In regards to his true name: Crowley doesn't remember it, and nobody really knows it either. The one who'd most likely know is Him, and who knows what He's up to these days.
→ Is still on Hell's payroll even with the averted Apocalypse, although he's been more of less regulated to clean-up duty - clearing up six thousand year's worth of near-and-then-subsequently-averted Apocalypse paperwork. Sometimes he has to team up with SPN!Atropos too since Fate has essentially been rewritten due to everything changing, although she tends to bitch a lot. Crowley really doesn't like that.
→ Besides clean-up duty though, Crowley hasn't heard much from Below these days, which kind of worries him because he's never received that long of a silence before. He has a feeling that something's brewing, and he doesn't know what it is.
OTHERS → With regards to Aziraphale - Crowley will never admit this to anyone (or even to himself), but he does have a bit of a crush/liking/fondness for the angel. It's partly the reason why he ever agreed to the Arrangement in the first place, why he stuck with him throughout all these years and why he stood up again the Apocalypse when it came. What he wants to protect is Aziraphale, more than anything else. Not that he will ever admit this properly.
→ No, he's not the same Crowley that's over in Supernatural. That would be the real Crowley, given the fact that his demon name is actually Crawly. They've talked a couple of times though, but Crowley doesn't keep too much contact with him because America? America is a bitch to get around. A lot of sin though.
→ For SC, he'll be taken around the year 2008, somewhere during the third season of Supernatural and before Dean gets taken to Hell. At this point he's only heard rumours and whispers at best about the new Apocalypse, so knowing that it will happen is... well... not at all a comforting thought for him.
→ Has travelled to different worlds and realities before under Hell's payroll, and while there has met the likes of Zatana and that strange Magic guy who name he really doesn't want to remember. Still, Crowley doesn't really like inter-dimensional travel. It gives him one heck of a headache.