Hey there, thx for your feedback. I will reply to your points:

Change team in story mode: Try pressing left analogue stick. Should work with both PS and Xbox Controller. What controller do you use?

Game physics: Yes, they are not smooth. That's due to the low resolution style. You can feel the bumpiness especially on the first two tracks as they are off-road tracks. However, my beta testers did not mention that they feel unpredictable. How can it be improved?

TimeKiller end session: You drive 99 laps unless you press the trigger, which marks your current lap as the last one. You still need to actually end this lap like ending a race.

SemtexMag + Rockets: Both of them have a charge animation. Rockets are ready when the red part of the body finished sliding forward. It takes around 1 second. SemtexMag's take around 2 secs, you will also get an acoustic confirmation when ready.

Game design: Yes, it's super unfair. That is by intention. If you progress to Story chapter 4 and onwards, you will be asked for pretty unique tasks which you can either resolve in seconds and minutes, or get stuck on for a while.
This game is based on games of the 90s. Those games used to be unfair. Maybe you heard of Fatal Racing/Whiplash: Sometimes one or two of the 15 AI cars decides to drive the wrong way. If they hit you in a looping, your race is basically wasted even if you were the leader. Similar for another game called MegaRace 2.
90's games were dirty and unfair and I chose this approach for my game aswell.
I know that this style is not for everyone. You can play BallisticNG or RedOut to get a more WipEout alike feeling.

Back in the days, I also threw my controller when playing the original Tomb Raider as Lara would just not make a jump. There was no easy way out back then, no internet, no 50 other similar games to choose from. You had to bite yourself through.
However, once you beat everything, it feels very good