All Regarding the Brake light and Reverse light, this will be 2 things, all attributed to a break in signal from the bulb to the ECU.
1) As mentioned, is a break in a wire from the bulb housing connector (least likley)
2) Corrosion on the terminals or bulb housing. (Probably this)
I had issue number 2 and is easy to diagnose.
Open the boot and you will see on either side of the inside of the boot lid the 2 squares in the fabric where you gain access to the bulbs. Open this, and pop the bulb housing out of the rear headlight (Disconnect the wiring harness first is a good idea.
Once removed, looking at the bulb harness (So the bulbs are facing you), you should see a black plastic case with metal tracks running over the housing. These tend to rust up due to the seals in the headlight drying out and letting in moisture, thus corroding anything metal on the housing. If it is this, 3 options
1) (CHEAPEST - Remove bulbs and set to one side, place hole bulb holder in a tub of White Vinegar for 1-2 days, scrubbing with a wire brush or steel wool occasionally untill corrosion removed (This will work for a while, but ultimately the corrosion will come back.
2) Purchase a new bulb housing from Audi (Or online) and it this. Corrosion gone. problem gone. HOWEVER, unless you sort the reason for the moisture ingress, you will get the issue again. BTW I though Audi would rip me off, but turns out they were the cheapest. Housing only cost around £18 last year, everywhere else on the web wanted £25+
3) Best Option - As above but also remove the rear headlight unit aswell. Remove the dried up seals (Foam like material), rub down lightly and attach brand new seals. Again, Audi were cheapest. Seals were around £8. along with the bulb holder it was £25 all in. and job satisfaction.