HELP- Audi A1 TFSI automatic

Hi
I need help, please.
I have an audi A1 2010 automatic car and I am having the following issues:
1st: when the start stop is on it is struggling to re-start the car once it stopped and sometimes it can't even restart it. Unfortunately this issue also comes up time to time when I am starting the car and turn the start stop off, however when the engine is warm and the start stop is off, it is fine. When it is cold and manage to start, it sounds like a tractor for the first 2 minutes and it is fine after that.
2nd issue: the aircondition button is not staying on. It lights up but as soon as i take my finger off it turnes off.

I have recently spent a fortune on this car because of these issues as my mechanic has no idea what it could be. We changed the timing belt, put a new compressor in, filled the aircondition up with gas and the issues are still the same.
Please help me.

If you had the same issues or know what it could be please let me know. I don't know what else I can do.