1:
My definition of an Edge router is one that connects to another providers network.
For example I may have 20 routers in my network. They will all have multiple routes so know where to get to different subnets in my network but I may only have one of them connected to AT&T. AT&T is a provider that I pay to get routes that are not on my network.
2:
If you are small (3 routers) then you may want to just start out with static routes. You will soon grasp a good concept of routing and hopefully the understanding this does not scale well. When that happens you want to start looking at routing protocols like RIP, OSPF, BGP.