I have the PC server (mine), my Wife PC, and the NAS for the Media Library in another room.
As we did a whole Home renovation I plan for cabling the house and put additional recessed gutters that cross between rooms.
This way I can throw myself cables (ethernet, hdmi, USB) as required, from one room to another.
If you have a room dedicated to office, where you have your working place with your PC, in a different room than the Listening/Watching room, it could be better to locate the NAS near your PC and have access from the Listening room just through ethernet. Asuming you can do the cabling. You have to plan then for switches to have enough ports to connect.
With respect to the noise, as soon as music or movies play a little, the sound of the NAS should go unnoticed. Of course it depends on what you consider annoying.
In my case, I was afraid of the fan of the projector noise, that is really a lttle high. I do not have the projector enclosed in a cabinet. But when music/films start to sound the projector sound dissapears.
For low volume music critical listening, I then turn off the Projector and start the TV for player navigation. Thats much better when I want silence.
I think there would be no problem in power ON/OFF the NAS several times a week. Someone have said in the past that specially the HDDs could suffer from start/stop many times more than beeing ON all the time at its constant temperature. But with modern disks I belive you can do that without any problem. If the disk is going to fail it will fail because it is a bad unit, and not because power ON/OFF every one or two days.