Is the g34 enabled to use a cisco ethernet connection?

Both the G34 and the SGB6700 are modem/router combo devices. You can disable the router portion of both but not the modem side (as far as I’m aware). 

Not sure what you mean by an M cell for phone usage. Are you talking a a microcell? If so, it should. there might be some setup needed to be done on the microcell. 

And more details on the cisco ethernet connection. Cisco’s a company and ethernet connection is just that. Are you talking a specific device from them? if so, which one? Most switches should work fine. Again, it might take some setup on the cisco if its a managed switch but the unmanaged should just be plug and play.