Solved

Tired drivers

I accidentally trained my drivers so they will have 60-65 health when my next race comes. Will it have a negative influence on their performance? They have 2 and 3 stamina.

Yes, if you train to much before the race they won't perform as well.
You have to train your drivers after the race so that they can recover to 100% during the day before the next race.

Depends if this was fixed or not.
https://igpmanager.com/forum-thread/8304

If it was fixed, then you will be slow drivers with no health.
If not, then you will have full health drivers starting the race.