In answer to
1) This is one of the reasons DTV/DSL is going away, they underpriced some of their offerings, a static address will be about $10/month anywhere. As they are all resellers
the modem may belong to the local provider (read your contract carefully, Just because hughes hasn't told you to return it , does mean they won't try to charge you for it, they have a long history of mis -communication

))
A static address is needed , if you are running a web/ftpserver from home, or for some secure remote appilications, otherwise dynamic is fine.
As a DSL modem is a usually a bridge from a PPPoE WAN your Router/wireless gateway/ NAT box will set your local addresses, your broadband IP will not affect it.
2) As I said above, the phone company may own it, or you may be about to pay for it

But usually the DSL provider provides the modem, hense no market for other brands/aftermarket modems. Cable on the other hand usual charges rent on the modem seperatly. If you plan to keep the service for a few years, believe the modem won't die for a few years, know the cable company won't change equipment require an upgrade for a few years, it might pay off to buy your own. if the rental is month to month, try the service for a few months to be sure you are satisfied with the quality of sevice
As far as cable vs DSL
Cable has more potential bandwidth, and have very low ping times (important for gameing), but it's a shared resource ie: when few people are on your loop speed s may/will be very fast. but in the evening when everyone else is on throughput may drop to near dial-up speeds! Even though local loops are upgradable for more capacity
ALL cable providers are currently losing money on the services, so upgrades are coming slowly and price increases are coming.
2) DSL is a dedicated loop to the local switch, so to that point the bandwidth/speeds can be garunteed, the service beyond that depends on their network, but generally speeds are very consistant around the clock.
Modem is usually provided/included in the monthly fees
All the RBOC's (local Phone co's) are making money on DSL, and the technology/basic equipment/maintance is standard phone stuff. So upgrades troubleshooting and repair happen as needed.
The most important thing is how
YOUR provider runs their business. as you are happy with the DTV service it means the RBOC is well maintaned, so any reseller big enough to give good instant 24/7 tech support (with hopefully you'll never need) can provide the same service.
Wtih either ask your neighbors, other users of the service how well it works