Ba3ic

Hello! I need help with what could be the problem with my A5 2011 Quattro sportback 2.0Tfsi, there are multiple small ones.

Firstly i have a p0420 code, it comes upp and then disappeared. I have switched the second O2 sensor and nothing happened, so i tried putting an extender on the sensor, read online that it helps sometimes. No code yet but symptoms are still there.
The symptoms i have are:
Slightly shaking when cold on idle
Bad gas milage
Excessive white smoke
When in D and applying the break it wants to go forward to much, and when i let the break go it goes too hard, but sometimes it pulls forward normally. When this problem occurs i can smell gas in the car when being at a stop for too long, usually i have to put in N.
"Gaerbox malfunction: You can continue driving, limited functionality" light once or twice a week, comes up for maybe 3 seconds and then always disappears. Gears works great nothing wrong that I can feel there.

Are some of these symptoms because of the same problem?
Do I need to change the cat?
Or could it be the TPS sensor?
The spark plugs are switched recently but maybe it could be the coils? Can they throw a p0420 code?

Im going with the car to a authorised mechanic next week to let them search through the car.
But I would appreciate if anyone knew something or have had the same issues, thanks!