I've got a network with several PC's and one public IP from an ISP. Can I run a relay on one PC and use Tor browser bundle on another PC?
Yes you can. You can even run TBB and a separate relay on the same machine (but then you have to make sure they don't both try to listen on the same port as a socks proxy).
The Tor instance that TBB runs only listens on port 9151 as a socks proxy for the browser. Your Tor relay listens to an OR port and optionally also a Dir port. You can specify those in your torrc. In your router you should forward your OR and Dir ports to the machine that runs the relay.