It is open to the public, one can just walk in. I have been
there a few times, and whenever I have nothing to do, I go there

I don't know of any restrictions about cameras... But it is a
museum anyways, so I guess there isn't.
The curator there seems to be very friendly as well! When I was
there for the first few times, one of them greeted me very
cheerfully and offered to show me around.