Not really sure how they do things with Rogers@home, but one of the two methods ought to work. Try setting the domain name on the router, computer name shouldn't make a difference but try it anyhow.
If no dice, then clone the MAC address of the NIC on the router's WAN port.
The cable that connects from the router's WAN port to the cable modem needs to be straight through. The router does the cross over it needs to do for it to work.
Not really sure what you mean. If you mean on the workstations, yes.4. I had the router setup as a gateway, is this right?