Push To Start Issue, Please Help

Hi everyone I just bought a used 2012 Audi A6 2.0 about 3 weeks ago it has 68,000 miles on it. We bought it without the 3,000$ extended warranty as there were no check engine lights on or anything. Well a few days ago it started having issues starting with the push to start when it asked if the key was in the vehicle we figured it needed a new battery. So we replaced it and it drove fine for that day.. weird the next Saturday started the same things here’s what happens.
we press the brake to engage the push to start and push the button and it will pop up about 4 codes.
TPMS Malfunction
Stabilaztion Program Fault.
Transmission Error: You Can Continue Driving.
And something regarding the headlights..
Also the check engine light flashes on.
Takes about 5 more tries to get it to start after it off for a minute or two... and when we drive it all the the lights and error messages turn off and it drives smooth and perfect..
anyone have ave any idea what could be going on? I’m not a mechanic but it seems like a computer issue no way all those codes are accurate..
please help before I have to go spend a bunch of money to get it diagnosed!
Thanks in advanced.
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