Checks will be done on a car-by-car basis, but once they are checked at the track, they come back to the lounge and are forbidden to enter the car settings page. In fact, I may as well use a permanent reverse grid format like in BST, but begin the series with a special qualifying event (like a live time trial, players taking turns to complete two laps) instead of the first race, followed by the full second race using the grid.
Teammates may use different cars. Whether they have the same livery/wheels/bodykits is entirely up to them, although having some way to identify a particular team (an image, an identity) is encouraged, whether it be a shared livery, identical cars with inversed colours, or whatnot.