1. yes you can use the 1720s to connect the remote sites via a T1 circuit.
2. You could use a DSL Wic or an ethernet interface for the dsl modem. The DSL interface would be preferrable, because you can see the DSL interface go up and down. Otherwise, the modem dsl is down but the ethernet is up. The router can only see the ethernet up. This would be more of an issue if you add a backup link for your internet.
3. You need to run a routing protocol or use static routes to point across the T1.
Site with internet requires:
T1 Interface
Ethernet interface (connects to local switches)
Ethernet/DSL interface for Internet
Site without internet requires:
T1 Interface
Ethernet interface (connects to local switches)
Another option would be to forget the T1 connectivity.
Add an internet connection to the other site. Create a VPN tunnel across the connection for internal traffic. Internet would go out the local router.