What is a rough shift

You may have a throttle position sensor starting to act up. That's the system anyway. The unfortunate thing is, you have to replace the entire throttle body. Unlike most cars, it's not removable. On the fan....do you mean it's constantly loud like an airplane or big rig?

Here's a link to causes of P0102. https://www.obd-codes.com/p0102

Most likley the seals round the injector sleeves have gone .

I would take the vehicle to the dealer and leave it there. Period. Tell them you don't want it back or even a phone call until it is properly repaired.

I would definately suspect that, and also the master cylinder associated with it.

The damage potential is with accidental shifts out of PARK, such as with kids playing around or the accidental shift by an otherwise occupied driver. To prevent accidental shifting out of PARK, car makers years ago started installing the safety interlock which requires a foot on the brake pedal before shifting out of PARK and putting the car in motion. No damage potential in shifting between other gears, as long as the vehicle is stopped. I hope that this answers your question and wins the debate for you.

internal transmission failure. if you take this to the dealer they will only replace the transmission. You might look for an independant repair shop that specialies in german transmission repairs.

if the rpm is higher than normal it's definately not shifting right

first things first, check your fluid level, and condition. If its abnormally bad with small fragments of black, you can assume that you burnt out a clutch and you'll need to get a reman or new transmission. If the level is too high or low, it will cause it not to shift properly.

Been there, Done that!!! Bought a 2000 bonneville used..once the car warms up it starts shifting rough and down shifting rough. I drove it all the way to work and it ran like a champ till i started start, stop drivin in the street and the tranny warmed up. I retured it to the dealer and it is a solenoid in the tranny that pumps the fluid to detect the shift pattern. that is what they fed me anyways. they fixed it for free. it wasnt too cheap..i got the slip and it was around 1300 dollars. im no car expert by far but this is what happened to me! hope it gives you an idea