I'll do the food suggestions:
Savoury:
- pierogi, try sweet and savoury (dumplings)
- golambki (rice and meat balls wrapped in cooked cabbage topped with tomato sauce and usually sour cream)
- placki ziemniaczane (potato pancakes, savoury)
- tatar
- really anything
Restaurants to try:
- Pijania wodki i piwa (drinkery of vodka and beer)
Pijalnia Wódki i Piwa ridiculously cheap shot bar with good drinking snacks. Try the Tatar and toasties. Menus in English too. See below photo with all the shots.
-bar mleczny (milk bar). They're not like ours, they're a communist era-relic with zero customer service. Delicious home made food and heavily subsidised by the government. See below photo with all the food.
- podwale 25
Restauracja Podwale 25. Kulinarne serce warszawskiej Starówki czeka na Ciebie! Tradycyjna gościnność, kuchnia i piwo! there's a few of these around. Bavarian style baked pork knuckle with all the trimmings included - you just order the pork for silly cheap prices. See below photo with the knuckle.
- any dedicated doughnut shop. Just bliss, especially when warm.