1. RV campgrounds - Just one or rotate, likes, dislikes - We have stayed at the KOA and Grizzly in West Yellowstone. We don't have children so we don't need all of the KOA pools/playgrounds/etc. Grizzly is in town. We preferred it to the KOA. AND I think it was cheaper at the time.
2. Getting around with/without a car - We took the car. There is a lot of traffic at times and you will want to pull over to see the animals. It's a lot easier in the car.
3. If only 7 days top 5-7 things to see - Yellowstone/Great advice to visit the Visitor Center first. Yellowstone is in a figure 8. We divide it into fourths. We try to see about one fourth a day. Read the signs at each attraction. They are good at letting you know how far each attraction is from the parking lot. DON'T leave any food (gum, chips, drinks) in your car. Even in the parking lot! You will want to see Old Faithful, the waterfalls, mud pots, just like the earlier post told you. Also, you will want to drive to the north gate and see the rock entrance. Mammoth Springs is also worth seeing. Tetons/be sure to take the boat trip on Jenny Lake. I think you can take it to the other side, get off and do a hike to a waterfall, and then boat back. You will need to check on that. See the chapel. Across the parking lot of the chapel is a historic cabin/store/ferry. Watch for wildlife. We stayed in Idaho when we visited the Tetons, only because we couldn't get into Colter Bay.
4. Cell and hotspot reception? Ok outside of the parks. Our phones are Sprint. Our hotspot is Verizon.
5. Tips and advice welcome. / Have extra batteries and memory cards for your cameras. Take a good pair of binoculars/sunglasses/hats/umbrellas/good walking shoes/jackets. You could be in snow and 90 degrees the same day. We always pack our lunches/drinks/snacks (sealed and in the trunk). Don't take your eyes off of the scenery! Animals blend in so well with the trees.
Have a wonderful time! It is our favorite place to go!