Unfortunately it is smoking. Smoking cessation stores are few

Yes, they have 2 shops @ishigaki

The regular holiday seems to be Sunday I could not enter without making a reservation If you have a plan, make an early reservation.

closest parking lot is.next to the museum 博物館 @100 yen per hour from there 3-4 minutes to Ishigantoten

Just before the opening time seems to be good.

No one will answer the phone. Go knock on the door and try your luck.