Yes to both your questions I went there two weeks ago
Adding on to other answers, they will send you back if the beach gets crowded. Also, bathrooms are open
The parking near by has the bathroom. Not sure if they are open or not. You can try
All open. Spent the weekend there
The park is open and bathrooms are open. We camped there last week.
Bathrooms by the jetty were open when i was there last week. Camping areas are closed, so those bathrooms may not be open
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