Thanks for the shout-out! I do have a couple of different metas relevant to your questions, and I'll link them as I try to answer the questions as best I can:
Tim was a little shorter than average as a 13/14 year old, but mostly in the "artists want to make sure people know he's a kid compared to the adults in the room" kind of way. He is noticably a bit shorter than many of his friends, but like @jumbledjupiter pointed out, he's far from absurdly small. I think most character bios pre-New 52 put him around 5'5"-5'7", if I remember right.
I've talked about various Batfam nicknames before here, though mostly in the context of nicknames Dick has for everyone. Someone also helpfully made a slideshow that's more comprehensive (though it's a bit out of date now).
Every single food thing you've probably ever heard about is usually both pure fanon and ridiculously exaggerated. Dick disproportionately loving cereal is no exception.
*crying quietly* No, Tim is not a coffee addict. He's only drunk coffee like four times total in canon and they were all in passing.
On Jason and Austen: no. He was seen reading Pride and Prejudice in prison pre-reboot, but that's the extent of it. He does, however, have a (small) history of quoting various classics, so it technically is rooted in a canon trait...just, as fanon tends to be, wildly disproportionate.
Jason is, however, extremely tidy. The various times we've seen his room and safehouses in canon, they've always been pretty neat.
The "Tim's room is a disaster area" thing is actually true, lol, or at least it was for a long time. While it was usually more "average teenager" than disaster site, as stated above, there were several instances where it was definitely showcased at disaster-level. imo it was an attempt to make him more "relatable," since artists stopped regularly drawing his spaces as disaster areas about the time writers started moving away from depicting Tim as a "normal teenager by day, competent vigilante by night" character (aka, during the Red Robin era).
No. Jason never thought Bruce was a pedophile.
Re: Jason's Titans Tower attack. Okay so canonically he showed up to hurt Tim for the funsies, because he hated (the concept of) Tim and wanted to prove he was better. Bruce technically doesn't actually factor into his hatred of Tim at all; he hates Tim for his own reasons. It's more complicated than that, but it certainly wasn't to try and scare Tim away from being Robin; Jason canonically had no interest in that. However, I think that the meta linked above isn't necessarily telling the full story because it sort of leaves out that the Titans Tower Attack happened well before Jason ever attacked Mia in Green Arrow: Seeing Red. This meta about pre-reboot Jason and Tim might give a bit better context about Jason and Tim specifically rather than just Jason.
BTW If you're more interested about Jason's mindset in general when he first came back to Gotham in Under the Red Hood, my meta here might be more helpful.
No. As stated above, Jason's eyes don't glow green. Also as stated, recurring, semi-permanent Pit Madness is also completely fanon and is not even remotely based in canon. Several Batfamily members have been dunked into Lazarus Pits with no long-term effects on various occasions, and Damian even explicitly states during the Reborn era while fighting a resurrected Bruce clone (sort of) that "any temporary madness would have worn off long ago."
tl;dr being dunked basically causes temporary madness and occasionally uncontrollable rage from a few minutes to a few hours after rebirth, but it's totally gone afterwards. Repeated dunkings over the course of centuries like Ra's has undergone, however, can screw you up.
No comment on Jason dyeing his hair bc it's been covered.
Yes, Dick is considered to be really attractive in-universe. It's actually become highly problematic in recent years because of DC's in-universe and IRL objectification of him as a character; canonically, for a really long time Dick was pretty self-conscious about his looks super uncomfortable with everyone continuously commenting on his looks/butt/etc. As writers and fans keep drawing attention to it, it keeps getting blown up into a much bigger thing than it used to be, and a lot of it is rooted in Devin Grayson's Nightwing run. This is a much larger discussion that honestly deserves its own in-depth response and links to multiple metas, but...yes, Dick is canonically attractive, and while it used to only happen once in a blue moon, characters comment on it fairly regularly now.
*sighs heavily* yes, the "Bruce cutting Jason's throat with a batarang" incident happened, at the end of Under the Red Hood. It's been discussed several times before by various people, though I can't find the particular meta I wanted to link at the moment; there's also been some really fun theory posts about how Jason died again at the end of UTRH, though not from the throat slice (hence why the final page of the arc's final issue is infamously left out of the trade edition, since it basically states that Jason died again in the building explosion he rigged). Basically...as stated above, Jason wasn't originally meant to survive outside of the context of that one story and editorial were giving themselves an out if his resurrection proved to be unpopular; since it was wildly successful, Jason instead showed up in the Nightwing book out of the blue about a year later, perfectly fine.
Yes, Damian tried to kill Tim a couple of times; no, the Batfam was not chill with it. The Damian-Tim drama is incredibly complicated (Tim and Damian are both right and wrong, basically) and a lot of people either don't know or refuse to acknowledge the full context. I've talked about it here and here (and...technically here, through the lens of Dick and Tim), if you're interested.
Zitka the stuffed elephant is fanon (though a rather sweet addition); Zitka the actual elephant is canon. We've seen Kid!Dick with a teddy bear before, though, and we know he and Babs both have a variety of Batman/Nightwing/Batgirl plushies!
That was...long, but I hope informative?
