Yep.
Oh yeah!
Yes, if they are apart of the ASTC Passport program than it should work. I would call ahead. "As a member of an institution participating in the ASTC Travel Passport Program, you are eligible for benefits such as free GENERAL ADMISSION when you travel outside of your local area. These benefits DO NOT include free or discounted admission to special exhibits, planetarium and larger-screen theater presentations, nor do they include museum store discounts and other benefits associated with museum membership unless stated otherwise." This is from the ASTC information sheet. Check and make sure your home museum is on the list.
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