If we have a lil party do we have to rent the spot. And do that go for the whole park?

Yes you have to rent the spot you have to pay for the area you want but what ever is around you you can use

Can I pay for the picnic today that I have

You need a permit especially if you are going to grill on your own units. Their way to know who left trash or left hot coals in case of a fire.

I would rent a spot if I wanted to guarantee that 1) I have a spot and 2) I have the spot I want. If that is not important, you can risk showing up and selecting from what's left.

Very enjoyable

Best to get a permanent that way you have nothing to worry about