Bottom Brackets & Cups

No. Bottom bracket shells in framesets vary hugely, depending on your bike / frameset manufacturer. They vary in both diameter, width and also in how they fit the frameset. Some are threaded (Italian or BSA British Thread) and some are pressfit. The best way to ensure a new bottom bracket will fit, is to look at your bike's existing bottom bracket and try to match. Check online for fit and compatibility if you are still unsure.

No, since the late 1990's, Campagnolo and Shimano have gone in different directions in terms of the bottom bracket to chainset interface.

Not necessarily, there are lots of smaller companies which specialise in specific components, such as Chris King, Praxis or Hope. Make sure the bottom bracket is compatible with the chainset and frame, and there shouldn't be any issues.