We spent 5 days there this summer. Yes it was hot. As mentioned the only CG with hookups is at the south end of the park near the Rio Grande. There are three FHU campgrounds at Study Butte/Terlingua. There are back country campsites that you could reach with a Class C.
As for how long it takes to see things, it's really a 4WD park. Or at least a vehicle that you trust on semi-rough dirt roads. The places to go on paved roads can be visited in a couple days. We spent one day driving the 60+ mile River Rd. We saw one other vehicle that whole day but it was summer which is the off season. I would not take a class C on it past the first few miles from the south.
There are some shorter roads that we spent a few days on. And there is the State Park to the west which is well worth a daytrip. Terlingua/Study Butte is a tourist trap area but has some restaurants. The have opened up the crossing to the small Mexican village across the Rio. That's near the campground. I assume you'll need a passport to cross.
Stock up on everything before leaving Alpine or Marathon. There is a small grocery in Study Butte outside the west entrance. You can get gas there or at one station in the park. Prices were about the same, I think the same company runs both.
This is a BIG park expect to do a lot of driving.