Could the control unit be at fault?
Have you done a diagnostic check to see if any fault codes flag up?
Here's the AC relay types:
https://m.autodoc.co.uk/car-parts/relay-air-conditioning-10463/audi/a6/a6-avant-4f5-c6
Here's a link to the fuses and relay locations:
https://fusesdiagram.com/audi/fuses-and-relay-audi-a6-c6.html
I'd recommend a diagnostic check to see if any fault codes flag up? Think the obd port is under the driver side lower dash. It could be a gearbox module issue.
What's the service history on the gearbox?
As degrading oil can affect the gear changes.
Just think, most people only come onto forums etc when they have a problem. As last Ng as it's been looked after you should be fine. For example my A6 is known for engine problems being the 2.5 V6 TDI. However mine has done 344k before failing. I know the history of the car as it's only been owned by my dad then me.
The tailgate water could be coming from the rear wiper motor. Definitely worth taking the rear panel off to investigate.
The tailpipes will either be screwed on or welded on. Only way to know it to look under.
20 inch wheels seem large. Are they Audi ones?
Definitely worth seeing if Audi wil stamp the book for you.
Look at YouTube videos for buyers guides.
Check for timing chain rattle on start up. Timing chain needs doing around 100k.
What's the service history on it?
Has gearbox and quattro system been serviced?
Do all electrical items work?
Have a look under A7 section as certain models can eat Dunlop tyres (first generation).
You'll need the headlights, module, possible wiring harness then get it coded to the car. For costings I'd recommend you speak to autologics or Audi retrofits as members have used them for retrofits and been happy with the results.
Not sure to be honest. Like you I did the same and have the rnse unit in my garage. However I'm thinking of going the aftermarket route as I like the idea of having Bluetooth on the screen and a reverse camera possibly.
It's not easy. You'll need the head unit, upgraded antenna, wiring harnesses, additional modules?
The simplest option is to fit an aftermarket android auto/apple car play touch screen.
If it has an alarm I suspect the siren will be in the boot side panel.
Electric aerial was standard I think as was the headlights on function. Even my old ford escort has that.
If you have a sticker in your boot it might have the different codes on it which would highlight the spec when codes are put in a decoder.
Think clear lenses were fitted to facelift cars if I'm not mistaken