Can you record and take pictures with your camera equipment?

Yes

The staff were fine with amateurt photography and even offered to take my picture next to a car. They also opened the hood of a car so someone else could take pictures of the engine. I'm not sure they would do that with all vehicles however.

I took pictures and videos as well. As long you don't touch the cars you are good.

You can record and take pictures for personal use. I would phone them if you have large equipment or intend to use commercially.

I took loads of pictures with my phone... Not sure if they professional photogs. Probably.