I'm planning on arriving on Thursday about 3 - 4pm. I try to find a pitch in the Southern end of the campsite, on the left side as you drive in about 100 yards from the shower blocks, preferably by a fence but not too much of an issue. I'd recommend that you bring something to rope off the "parking space" next to your tent otherwise someone will nick it to pitch theirs!
I've never left the car on the stand overnight, always bring it back to the campsite. It's somewhere to lock valuables up overnight or when you're going back into Silverstone for the music/entertainment.
Cheers
Guy