Can you wear open toed shoes?

Yes but I wouldn't

No problem people where flip flops everyday.

Not a good idea, IMO

I would not

Yes, you can but your feet probably will be filthy from the dust/dirt/salt residues that occur naturally in the mine. Make sure whatever shoes you wear are comfortable. It's a fantastic place! Hope you are as awed as I am each time we went.

Yes

I believe so, I don't remember seeing anything stating otherwise. I would call them just to make sure.