Are there tables at the rented sites? Or do I need to bring my own?

Every campsite/cabin includes a picnic table and a field stone fire pit. Go to www.bound4burlingame.com and click around. Its he best source for info. Its a website created by campers, for campers voluntarily. They have videos and photos of every campsite in the park.

Almost every single site has a picnic table and it is very low to the ground I think it's always a good idea to bring a fold-out table

There are tables. You can even rent an extra one.

They say there is a picnic table on each site but there wasn't on mine and walking around the park, there were several that didn't have tables.

You will need quaters to take a shower.

Every site has a picnic table

Each site has its own picnic table.

Yes