Hi Lil,
Each CP is different, but the 'camp kitchen' often has a fridge, microwave, toaster jug and hotplates plus washing up facilities. Never seen an oven.
Popular CPs often have a line waiting for 'camp kitchen' facilities, but if you get in early or late. No probs.
Utensils vary, often supply yourself.
I would assume stuff gets nicked. There are human beans in the park after all.
If you can, run your own fridge utensils washing up stuff etc, you will be better off. Also,be prepared to clean the hot plate before using.