I read that there is a $10 parking fee. Whats the beach capacity & how early should i get there to make sure i won't be sent back due to full capacity? Are there any restaurants or grocery stores nearby?

Yes is $10 for parking is better if you can go early before 10 am. And no i don't see grocery stores nearby is around 15 minutes outside.

Yes. No capacity for now. Go early park opens at 8:00 am. No restaurants or grocery store. Take everything you need and you'll have an awesome time. Also barbecue. 10 feet apart.