Will they allow a senior to take their time climbing up to the top or do they advise against bringing anyone who needs extra time during a tour?

Yes, it was not that crowded and you can take a self paced tour.

Yes seniors can go . It's a spiral very steep but every so often there is a landing with a window. Can get a little closterphobic though

I can't be 100%, best to call them. it is a good amount of stairs, but my wife is petrified of heights and took her time getting up, no one seemed to mind.