Take a camp chair or two and if you have a canopy take that, depending on the venue (for example I go to Roebling and there are no stands so seating is strictly bring your own if you want to watch). Will give you a shady place to sit and rest and watch the other cars in between your sessions. I always freeze a few gatorades and waters and put them in the cooler with the regular cold waters and gatorades, keeps them cold
See if you can ride with your instructor in between your sessions in his car; PCA lets you ride with instructors in one run group above yours. That can be very eye opening.
If it is your first time on a DE it might be scary the first time (it was for me) but by the end of it you will be ready to come back for more.
In my opinion chances for damage at car control and autocross is very low. When I go to a DE I get the lockton motorsports HPDE insurance, but I don't when I got to autocross (unsure if they even have it but I haven't looked)
Have fun!
Steve
Edit: my tips are for a DE, I missed the car control part.