Bottom round doesn't have enough connective tissue or fat for it to make a good cut for braising. It will sort of fall apart if cooked for long enough, but it's not ideal.

For the meat to fall apart the collagen needs to dissolve. In order to dissolve the collagen the meat needs to have an internal temperature of about 200 F for about an hour. Braising will keep it from drying out.

Oops, forgot the tomatoes in the Stracotto I described above. Gotta have the tomatoes.

Timing depends on size of piece of meat you're braising - two hours may yield a pot roast, i.e., still intact enough to cut into slices; braised longer, it will fall apart. I usually use brisket for Grandma's pot roast, but chuck or round for stracotto, the Italian version - braised with red wine, beef broth, garlic, fresh rosemary and sometimes porcini. Cooked until it falls apart, served over polenta or papardelle - seriously one of my favorite things to eat.

Yes it will. Use any combination of beef broth, wine, tomatoes as your braising liquid. Low and slow heat, covered, for a couple of hours.