Yes, of course. You can attach one router per any connection that your modem has. Normally a modem has 1 input connection (internet line) and 4 output connections (RJ45 standard network). You have to plug a cable from any of these connections to the Internet connection of your router and it will work just fine.
You can't attach the second router direct to the modem. Connect one router to the modem and the other to this router (1st router should have a switch).
Yes. It is commonly referred to as bridging the routers and can be done in different ways. No matter what router you will need to make some changes in the router settings. The brand tells which method you will need to use after that.