(1) I have to have a fan running for white noise, which cannot be used for obvious reasons
I too can't sleep without the "white noise". At the lab I went to, I was allowed to bring my fan (a floor fan), although I had to keep it on medium (I usually have it on high) so the tech could hear if I had a problem. They also had a ceiling fan and a bedside fan.
the room has to be very cool (more like frost on the blankets)
Me too! I was delighted when I walked into my sleep lab and it was VERY COOL! The tech said he does that so the leads won't slip off. Have you asked them at the sleep lab about this?
I have to go to the bathroom a couple of times a night. I wouldn't be able to go if I were all hooked up to monitors
That also sounds quite familiar. Before CPAP I used to get up once or twice just about every night to go to the bathroom. You WILL be able to get up and go to the bathroom if you need to. After they hook you up, they have a box attached to the leads. This box is attached to leads that are connected to the wall. They can unhook the leads between the box and the wall, and you can get up and move freely. If you have to use the restroom, all you have to do is call out and the tech will come and get you (I know, a bit embarrassing, but that's what they're there for
I would think the sleep lab would want to make things as comfortable for you as possible so they can get a good study the first ime. I don't think it would be unreasonable for you to request that the room be very cool or that you be allowed to bring a fan. If they are not willing to work with you, then maybe you can go to another sleep lab that will.
Hope this gives some encouragement to go ahead and have the sleep study, and puts your mind at ease.