I had a reservation to tour a museum, but the museum was closed on the scheduled day because of a typhoon and they won’t refund my ticket.

Ticket refunds are basically governed by the terms of service. The terms may state that if the museum is suddenly closed due to a typhoon or other natural disaster, you can reschedule and use the ticket at a later date (but no refunds are issued). If that is the case, you will not be able to get a refund. Also, the cost of the ticket may be included in the tour, so check with the travel agency.