Since public transportation will get you pretty much anywhere worth going within 30 min, here are a few recommendations:
A lot of places are closed on Mondays, so my beloved Henne is not going to happen for you, but if the skies clear early enough for Biergartenzeit (which they tend to do in Berlin… just in time for sunset ), get thee to Prater, Cafe am Neuen See, Schleusenkrug, or Ankerklause — all popular with locals and tourists alike, and you can get a nice brat, good potato salad & a pickle at Prater.
For Currywurst, Curry 36 is one of the classic sausage slingers, as is Konnopke (I’ve not been, but Bourdain has ). Konnopke is super-close to Prater, so you can do a lil sausage tasting if you feel so inclined.
You’ll find any number of Currybuden all over town, however. I wouldn’t sweat it if you grab one at a rando booth. It’s drunk food. Another very popular food is döner kebab, but being that you seem to have traveled Turkey excessively, I hesitate to recommend any Turkish food, even though it’s as Berlin as Eisbein at this point.
If you are into sweets I suppose you could get a Pfannkuchen, which is what Berliners (the donut confection) are known as in Berlin.
IF you are nearby, Rogacki is worth a lunch visit. Also easy to reach by subway.
Metzer Eck (same district as Konnopke and Prater) is one of the oldest Bierkneipen/Restaurants in Berlin.
As for supermarkets, the most famous of course is the food department at KaDeWe, but you’ll find German foods anywhere (REWE, Edeka, etc.). Not sure what you mean by “Fleischhauer?” A butcher?