1. Are there any reasons I should not connect a second network up and should just use a single roaming network instead?
It depends on your requirements. If you want to be able to "walk" a laptop throughout the house, have it pick the strongest Wi-Fi signal automatically, and stay on the same network, then you want a "roaming network".
If you want everything to work in a "roaming" configuration, it is often tricky to match up the exact wireless security settings on routers from different manufacturers. To work correctly, the wireless network name, security settings and password must match up exactly between all devices.
Most users know their wireless network name and password, but may not know exactly what type of wireless security that is being used. If the settings do not match up exactly between all routers, then you wind up with separate networks, not a roaming network.
If I do create a second netwrok, would I just plug the ethernet cable from one of my walls into the Airport Extreme?
You would "create a wireless network" in Bridge Mode no matter whether you wanted a roaming network or separate network.
If you want a separate network, assign a different name to the wireless network. Computers will need to log on separately to this network.
I'm assuming that the Ethernet cable is routed back to one of the LAN ports on the "main" router. If that is the case, then the AirPort can plug directly into the closest wall jack.