Is the entire park open or only parts? If some areas are closed which ones?

Most if not all of the park is open including most stores and restaurants

All is open at universal and islands of adventure

I was just there this past weekend and Universal Studios is fully open to answer your question.

Volcano bay is closed but all other parks should be open

All the rides are open volcano bay opens in the beginning of March.

Volcano Bay is closed.

The entire park is open except for Volcano Bay but that is just for seasonal reasons and not due to corona.

Quite a few shops are closed but all the rides are open