tim drake is a rare case where every wild, out-of-context thing you hear about him gets even wilder with context
made up a fake uncle to avoid getting adopted? first he had to steal his dead dad's will and change it to include the name of his fake uncle, then he forged an entire legal paper trail to fool even batman, and finally hired an out-of-luck actor to play the uncle and had brainstorm sessions with him about his character backstory. judging from his surprised reaction when bruce offered to adopt him, he probably did this to avoid being put into foster care and didnt even consider that bruce might want to adopt him (even though he already adopted three orphans before him) (and then bruce learned about this and gave him more freedom and crimefighting gear so tim could like him)
snuck into gotham during no man's land? he did this twice, first by himself to meet his girlfriend in the hospital while she was giving birth (he snuck into the ER as a nurse), then with his young justice friends who thought he was having daddy issues with batman and wanted to help (this was before he was adopted by bruce) (they also picked up an atlantean tourist on the way who wanted to sightsee gotham)
blew up several of the league of assassins' secret bases? before that he spent days working with them as a member to gain their trust (this was when he robbed that art museum) and all the while they were holding his dad's coworker's daughter who came to search for tim and learned about his secret life as an assassin before she learned he was robin (and then somehow fell in love with him)
becomes evil batman who kills in the future? not only that, he also convinces his friends to be evil with him and then takes control of half the country right after he kills every rogue in gotham and also his aunt. tim fought this version of himself at least three times, and each time swore that he would never become gun batman (he still becomes gun batman)
used his own legal last name as a hero name? he didnt even come up with the idea for that, he met an alternate earth version of himself (also evil) who was using that name and thought "oh that's a good name" and stole it for himself. he didnt bother to check if other drake's identity was public before he started using it. then he got pulled aside and told off personally by batman for using such a dumb name and that's why he's not called drake anymore
insulted jason to his face while he was trying to kill him? did this multiple times and even kicked jason in the nuts once (not while they were fighting, just as payback) (he's jason's favorite brother now)
and then anything that happened with young justice doesnt need any context because it's exactly as weird as it sounds. yes, he did save the fate of a planet by playing baseball with his friends. yes, they did invade an entire sovereign nation to rescue their one friend's parents who had turned into babies. yes, they did see santa claus die in a fiery explosion