Yes
Yeah, but be polite, quiet, and respectful to other people for goodness sakes!
The security won't let you block or disturb others viewing.
I'm not 100% sure about video. They do have signs that say personal photos are ok, but no flash. It won't hurt to take your stuff and just ask when you get there.
You may do so in a very polite way and with respect but you may ask one of the docents on site
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