Hello! First off congrats on getting a projector. I have had my projector for about a month, and I love it to death...
I am no expert myself however, so take my answers with that in consideration.
I do not think there would be a problem with you mounting the projector in another room and then cutting a hole in the wall. After all, when you go to the movies, isn't the projector in a projection room with a hole cut in the wall of the theater you are in?
As for the size of the hole, I don't think anyone other then someone who does this stuff for a living could estimate that. Perhaps the best way to do this is to just try making a template.
I would first see how far off the wall in the next room you are going to place the projector and take an accurate measurement. Then after that, throw a small image on just a regular wall and take a peice of cardboard and cut a hole in it. Place the cardboard about the same distance as you measured and see how big of a hole is needed to not disrupt the image. Then you will have a somewhat accurate idea.
This would be my guess for working with your current setup. Sorry if none of this helped you, I wish I was more knowledgeable on the subject. Good luck.
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