Yes you can sweat underwater.

As for the moving bus, you would land somewhat close to where the bus is when you land. If you take out of account air resistance, you would land next to the bus. This is because you're moving with the bus, and so when you jump out, you are essentially moving forward at whatever speed the bus is moving at too. Just like how if you're standing in a bus, and you jump, you don't not move, the bus moves, and you slam your back against the back wall of the bus. You stay in the same place on the bus that you were before.