The engine temp gauge read normal. As it could be the thermostat.
In failing that you could do a diagnostic check to see if any fault codes flag up as there could be an issue with the heater module, control unit etc.
Check the service history. Is it full?
Has the gearbox oil change been done on time.
Has the quattro system been serviced on time.
Do all electrical items work?
As they can be expensive to fix.
Does the AC work.
Check YouTube for buyers guides.
Sounds an electrical.fault. How old is the battery?
As old batteries can cause all sorts of electrical issues. Especially if the alternator isn't charging it?
It depends if the car is set up on long life servicing or not. Audi would be able to tell you. And inform you of all the work it's had in its life by Audi.
Filter change may depend on engine but I think it's roughly 5 years or 50k. Whichever comes first
Could be the heater control unit.
Contact Julius from this eBay link. He breaks c5s. I've had bits from him. Very helpful.
https://www.ebay.co.uk/itm/163720125396?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=J_mXsPy2Qdi&sssrc=2349624&ssuid=IE07kO4STZy&var=&widget_ver=artemis&media=COPY
If the eBay one never turned up I suspect it was probably coming from overseas.
I always look at UK sellers.
You could always get your current one painted.