I can only answer a bit, since it's been a long time since I've stayed at the Beach Club (but have stayed at the Boardwalk Inn and Villas more recently).
I would call reservations, and explain the sensitivity to noise, to ask for a room at the end of a hall, and on a high floor, and hopefully not connecting to another room, to assist with it being more quiet. I'm sure explaining this is a medical need, they will at least note it and do their best!
I find walking to DHS long for me (after all the other walking), but I do it at times. Mostly I take the boat, though.
Refill mug:
https://disneyparksmomspanel.disney.go.com/question/fill-free-refillable-cup-yacht-club-312397/
You can refill your mug at ANY resort. So if you're at the Boardwalk, there is also the Boardwalk Bakery (not worth the trek just for that).
Oh and just found this:
http://www.disneyfoodblog.com/2017/...-at-ale-compass-in-disneys-yacht-club-resort/
So no, you do not need to go outside to refill your mug!
I read there is still sand bottom area. We tend to prefer the quiet pools (if we swim, which is maybe once a trip).