My friend , it sounds like a LEMON to me. Originally, probably was just a battery or Alt. to begin with. Because these damn cars using or consuming lots of power even in park or ignition off until it goes to sleep. Thats when everything is off. Think about on most cars only need about 450 amps to start and these 7s' need 850 amps ( a least that's what shows on the battery itself. )
If you were to do a draw test on the battery on these cars, you're gonna go NUTS on it.
So....If I were you, I'd bring it back to the dealer where you got it from. Then go from there. See what they can do to fix all this.