SSID can be set the same, the computers are smart enough to hand over to the router with the strongest signal.
If you want Router 1 to reach other rooms, you should set your rates lower. 5ghz doesn't penetrate walls as well as 2.4.
Router 2 should be setup as
Bridged mode, basically you set the gateway etc as if it is another PC connected to Router 1.
It depends on which firmware your spare router has. OpenWRT or Buffalo is the most flexible.