Does my dog have to be leashed? Is there fencing? I have a puppy that still doesn’t come all the time when called.

There is a fence, dog does not have to be leashed. You could take your pup to the small dog area to begin with, it is smaller, you might have better control

Your puppy needs to be old enough to have it's rabies vaccine and a license.

Yes please be aware that there is a minimum age limit. For the park. I think it's 3 or 4 months.

No and yes.