Should be fine as long as you keep things away from the car surfaces. As someone else mentioned, no photos in the vault.
I would assume that picture taking is encouraged. The staff there were super friendly
I think so. If you do the vault tour you can't take pictures or record though. Hope you enjoy the museum, its really nice.
I took MANY photos with my smartphone and there were no issues. I bet if you don't make it a big production and block someone's view it will be okay. I would confirm with the desk when you get there.
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