Theoretically, yeah that should work fine. In practice, well, it depends on a lot of things. If you're living in Manhattan, chances are your building has pretty old electrical wiring, which could cause problems. Remember that powerline reuses the wiring for power that's already in your walls, so it's almost impossible to upgrade without a complete renovation of your building. If I was in this kind of situation, I would probably just run an ethernet cable all the way from the basement to my apartment, and either get a cheap wifi router to broadcast it to my devices, or plug it directly into my PC. Powerline is far from a perfect solution, but it's hard to gauge how well it'll work for you without trying it out yourself.
Very unlikely given the likely interference, circuit jumps, etc.. It also depends on wiring age. I'd rather suggest you try running an outside-rated ethernet cable or a point to point laser link down the side of the building than try a powerline adapter. Wifi boosters with directional antennae may even be more feasible than powerline.