Marion, the tunes you'll be learning are designed to be played solo. If there's no other instruments, long rests will sound pretty boring! But if there's 2 or more instruments then one can play harmony; in that case, the harmoniser can add in rests and stuff to emphasise the rhythm of the piece. Melody-player and harmoniser can swap over as they feel like it. Your duet will work the same way - at any one time, one will be carrying the tune and the other will be supplying rhythm, harmony, bass-line, fills, counterpoint etc.

The flatter the bridge is, the less distance you have to rotate the bow to get to the next string. As you say, there is also a greater chance of hitting duff notes though!

Grab.