I'm more familiar with older audis but you should start by looking under the engine for "fresh-looking" oil residue if its already pretty grimy under there. If it all looks the same take brake cleaner spray and a rag and clean it up. Drive a little bit and check for new oil and you will have a general idea of where the leak is. It's possible you are burning oil too instead of leaking.
As for the stalling, Idk is your fuel pump new, o2 sensor newish (good gas mileage?), does car do it everyday when engine is warm only or both warm and cold engine, does it do this regardless of temp outside? New spark plugs, cap, rigor, wires. Idk since I don't know the car. Is your oil pressure warning light coming on? Have you ever run fuel injector cleaner through those old injectors?
Lastly, don't put all your eggs in one basket and go to the audiworld forums too. This forum can be quite dead sometimes in this subsection.
1988 Audi 5000CSTQ, TAP, 2.5cat-back K&N CAI, 2.5 bar spring and bolt mod, AFR'd to 18 psi, IC sprayer, AEM W/M