The park is open from 8AM until sundown.

Edit: I was there yesterday. I asked the ferry skipper how they were getting snakes on a barrier island. Answer: They swim there, and he sees them occasionally just shaking their way through the water. Granted, that’s a little disconcerting, but the beach is a wide open space with zero shade. Not a place snakes tend to hang out. The interior of the island however has plenty of space for the slithery kind, so stay to the boardwalks and beach if you want to minimize the already unlikely chance of seeing one.

As you drive up the cause way you will see on the left side of the road a couple of places, before entering the park.

Frenchy's is before you drive over the causeway. Excellent restaurant with in & outdoor seating. There is also a little diner & an English restaurant in the shopping center. There is a subway & McDonald's in the s/c & an ice cream shop across the street on the corner, but you need a car.

Yes you can

You can either kayak or take a ferry to the island.

I do not believe so, but I would think it best if you followed the rules.