Professional photoshoots are not allowed. If you're suspected of doing so you will most likely be stopped by security
If you are taking professional photographs very likely you'll need permission to do so. I would contact their offices for more specific information.
Depends on equipment. A simple tripod and a DSLR were okay in my experience. Anything additional, like c-stands, lights, etc. - I would talk to the administration beforehand.
You might need permission if you are using your photos professionally
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