Berlin isn't really Germany. It's an international city like New York or London, and is essentially a city-state. Berliners are Berliners before they are German, and you'll hear a LOT of English on the street.
Best way not to annoy the locals? Don't be an expat or a Swabian. Berliners don't mind tourists, but some of them are not fond of Berlin's new status as the international "It" city as foreigners and Swabians are moving in and driving up their formerly low housing market prices. So embrace being a "tourist", no one will judge you.
Supermarkets are pretty close to the US standard, except that you bag your own groceries and your US credit card may not be accepted (chip and PIN probably will.) Smaller markets, bodegas, liquor stores, kiosks you should just plan on using cash. Same for non-fancy restaurants. Berlin is getting better about accepting cards than the rest of Germany but it's not fully there yet.
Berlin is spread out and the neighborhoods all have a distinct character. My suggestion is to spend a half day checking out an attraction in a neighborhood and then just walking around, browsing shops, cafes, restaurants, bars, etc.
For me, the former East is far more interesting than the West. I definitely recommend staying in the East.
There's not really a Berlin cuisine unless you're counting currywurst or "New German" which is upscale takes on traditional German dishes. Sure you can find plenty of schnitzel, but just as much burgers or Asian food or Turkish food. Go ahead and embrace it, German food gets boring quickly anyway. Berlin is an amazing food city for the diversity and price of the food.
Depending on the weather, Berlin has a lot of great green areas within the city and reachable quickly. So if it gets warm and you want a break from the city, it's easy to find!
Expect to pay 50 cents for public toilets, in museums sometimes, etc. Don't get annoyed, just pay it.
And just enjoy! Berlin is my favorite city in Germany. I could be there for weeks without running out of awesome things to see and do.