1. You hook the nomad to your router.
2. The nomad does not use one of your tuners.
3. No idea, but I use my iPad just fine with the current app.
4. Yes, you must call to get it activated on your account, but you can still buy it from 3rd party dealers. Last I checked, SolidSignal sells them for $99. Some have reported delays in getting a used nomad activated on their account; so you might only want to buy a new unit.
Regarding number 4, I don't recall having to call DTV when I activated my GenieGo. As I recall the app does it when setting it up - although that's just a difference in semantics, as the app is still "calling home" but online vs using a telephone.