Time trial leaderboards are located at https://mariokart64.com
VC versions are also allowed for time trial submissions if you have one of those systems to use
It's mostly because it would be such an incomplete leaderboard that it's not worth tracking for us. Even the N64 cup categories are really just there for tracking WR history since people typically don't go an extract the cup times from their full game runs. Cup runs take significantly more moderation work too. Because of the fact that a lot of submissions are from full game runs, mods have to more carefully retime the runs. Of course, you can play the category without the leaderboard too if you really want to play cup runs.
Yes, you can keep retrying. Usually just worth resetting at that point, but you can definitely submit a run with multiple attempts on a track if you'd like.
The place to submit time trials is mariokart64.com Unfortunately you're looking at the wrong time though. You're playing on an NTSC system while comparing to the PAL world record. The current NTSC record is 26.01. The current PAL WR of 30.92 is equivalent to a 25.72 on NTSC.
I'd recommend turning a little to the opposite direction before hopping into the slide. Like if you were on the start of Luigi Raceway and wanting to do left-facing MTs, before jumping into the slide, angle your kart a bit to the right so that your angle when you complete the MT isn't quite as bad. Over time you'll improve and won't have to angle the kart as much before jumping into the slide.
Do you just mean MTs in general or specifically SSMTs (straight stretch MTs)?
The time trial world records are significantly stronger than you might think. You're playing on the NTSC version of the game but you were looking at the PAL WR time which is equivalent to a 1'37"95 on NTSC.
The best run actually done on the NTSC system is a 1'38"17
Yeah, nothing weird for the Switch release as far as I could tell (at least in single player)
Yes, you can submit both and they'll get filtered into those sections if someone is viewing those regions directly
Yes this is very well known and is even mentioned in the time trial rules: https://64.mk/mk64/rules.html That being said, it's considered a shortcut which makes it useless since there is a much better shortcut in the cave.