Are they open on Good Friday?

I would call to be sure, but they likely are.

Yes I believe They are. They are open almost everyday of the year.

Website says they are open 365, but calling to be sure is a good thing to do.

And be sure to see the David ...

Yeah

Yes, go today or tomorrow to see the Marilyn Monroe dress.

In all my 50 yrs of coming to St Augustine I've only seen it closed once, for repairs.