As far as I could tell, no one cared what you're sleeping arrangements were in the parking lot (I was in a pop-up tent trailer with the beds pushed out front and back, though I was still attached to my truck). Possibly a tent might be pushing it too far.

I don't see why not. There were several cars parked overnight in the lot when we were there. Obviously I didn't check if they had occupants, but I didn't see any problems.

I don't see any problem. Just pay for the time you'll be parking. You might attract unwanted attention if you have an outdoor barbeque or a portable fire pit, or a popup tent.