You can get to it from within the hotel and you have to pay $15 a day to use it as a hotel guest. I presume they are separate legal companies and the gym is just like a concession in a department store. Depends what you mean by affiliated really and why you are asking.
It was free for me
Just join the fairmont President's club (free) and there is no $15 fee as complimentary gym access with membership as long as you're staying at the hotel at the time you use the gym
I don't think so.
I'm not sure, sorry, we live local, and try to stay a few days a year, so much heritage and all the presidents stay here for 100yrs or so, many pictures in the hallways
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