Weekends can become busy, and there is a line inside the museum for tickets/passes. If you don't want it to affect your museum time, I would recommend arriving 30 minutes to an hour early on purpose.

Yes on water stations. Membership package numbers are generally based upon each visit. The trend in museums is to define packages great for couples, families, grandparents bringing grandkids, etc. Maybe at some point they will figure out a "singles" looking to find a single might work too!

I did see a water fountain, but not sure it is filtered.

I’m not sure. Both entrances have a flight of steps but I didn’t notice if there was a lift. Sorry not to be more help.

Not really. Saturday is busier.

Possibly, but give them a call to be definite.

Yes, IMAX tickets can be purchased separately.

we didn't eat nearby, but the man at the information desk gave us a few recommendations including one with the name "Cherry" in it that looked really interesting

Had lunch at the café and the soups were good

I maybe too late to answer your question, but I went to exhibit on an after 5pm admission. It was fine. The staff controls admission so that exhibit is never crowded and is more extensive than DC Presentation is great and very detailed! Restaurants all over as well as Whole Foods with a great buffet and some small specific food stalls (i.e. Chinese, Mediterranean)