I can help you with some of these;
1) The 86 isn't a particularly fast car, but I'm pretty sure it is faster than the MX-5. Not sure exactly, what's wrong, would have to see a video or something. (You said you have TC off, maybe you still have Stability control on?)
2) This game is optimized for a wheel. It does support keyboard, but I feel like a lot of your handling issues are because of it. I'm not sure how well you can perform with keyboard when it comes to steering, and throttle + brake control is impossible when you've only got an on-off switch.
3) What do you mean by quick race with your own car? It's possible to set it so the grid uses the same car if that's what you mean.
4) I presume they're like drag lights, the actual "go" light isn't consistent so it forces drivers to actually react instead of just timing it properly. Do not know if real race track lights work like this.
5) All AI use stock cars as far as I'm aware, changing the strength/aggression doesn't change car performance.
6) Gear changing in AC is slow because like you said, it simulates the clutch too. GT Sport is a bit more arcade/casual than AC so it'd make sense that it'd be faster, but in AC you're at a major disadvantage if you don't have an actual clutch and shifter.
7) It might be possible to only use h shifter if you don't set a paddle shift button, but I haven't tested this myself. Some cars have more gears than a gear shift has though.
Don't know about the last two, although i'd like to know about any tach mods myself.