When I set up a hidden service with Tor, will all clients connect over the same connection between the hidden service and the first relay/router? What is the bandwidth that I can probably expect?
When you offer a hidden service, your Tor proxy builds a circuit to the rendezvous point. The client which are connecting to your service also build a circuit to the rendezvous point. The rendezvous connects both ends of the circuit (see the hidden service protcol). You as well as the other side will probably have different relays which they are using.
I'm not aware of bandwidth estimations. However if you offering a popular hidden it may consume a large portion of bandwidth. Silk Road was one of the popular places. The site Silk Road: Theory & Practice has some further reading. They link to a paper »Traveling the Silk Road: A measurement analysis of a large anonymous online marketplace«. Maybe you can find some traffic estimations there.