How to calculate the minimum number of groups, by grouping groups with capacity together?
The problem is NP-complete, because in the special case that all cars have the same capacity, it is just the bin-packing problem. 

If car A has a higher capacity than car B, and you get an optimal solution (smallest number of cars) containing B but not A, then you can swap cars A and B, you won't need more cars, and because A has more empty capacity, you may fit the passengers from another car. So which cars you use in an optimal solution is obvious. You use cars sorted by capacity in decending order. So no matter what the numbers of passengers are, you would use the car with 7 seats, then the car with 3 seats, then the one with 2 seats. I assume you have groups of passengers you want to keep together, otherwise it is trivial.

You should be able to adapt any bin-packing algorithm to your situation. I can't see graphs being useful in any way.