RAF lakenheath has 90 (UK 94) octane fuel, RAF Mildenhall has 94 (UK 98) octane fuel. The two bases are about 5 minutes away from each other so it's no big deal to hit up Mildenhall for fuel.
Your car will fit just fine as long as you get a house with a driveway, or some other way of parking off the road. There are plenty of American SUV's that work just fine, your main problem will be parking.
You will not find any parts for the Camaro over here. There are some performance shops, but nothing like you are used to in the States.