Can you swim on the beach there

No, but you can swim in the water directly adjacent to the beach. The beach is, in fact, a solid.

If you staying at Hotel Breakers, you can use the beach and water until midnight.

I don't know. It looks like a private beach from Cedar point park. I'm not sure of the name of the beach either.

Yes

Yed

Yes. The beach is open for swimming. Remember that parking is $20.