Is there seating within the galleries themselves (thinking of elderly who can walk but need to rest often)?

There are bench type seats throughout the galleries; there could be more but some spaces will not allow it because of size. I have those same issues and was not inconvenienced at all.

Depends from gallery to gallery. Some, but not all, have a bench in the middle of the space where you can sit and enjoy the art around you

Not in all galleries.