Not sure why, but your post did not appear when I was browsing the forums last night. I expect it was the same for everyone. Having said that, you are asking difficult questions
Having too much carpet on the walls would probably hurt your sound -- the issue is that carpet absorbs the highest frequencies but lets the midrange and lower frequencies still bounce around. Most of the "more knowledgeable than me" folks tend to recommend a mix of absorbent and diffusive surfaces, ie if you have a lot of bookcases full of CDs and books along the side walls that would be OK but solid carpet would probably make the room sound funny. The best would probably be alternating panels of carpet and wood, making sure that you have carpet at the "first reflection points" (something for you to Google
).
Regarding insulating under the carpet, seems to me that the very best would be to put in rigid fiberglass panels and apply the carpet right over that without wood in the way. Alternate that with wood panelling and I think you would get great results.
Screen selection seems to be a bit of a black art but from what I can see the best solution for viewing with a few lights on seems to be screen gain (ie something which gives you a brighter than normal image as long as you are not sitting too far off to the side) as long as the lights are not behind you. The need for grey seems to be a function of your projector's contrast levels and how light the walls/floor/ceiling are around the screen -- I don't know enough about your projector to advise there.
Since the room is pretty much square you are going to have response peaks around 40 and 80 Hz. While this didn't seem to work for Randy (sirquack) I would think about locating the sub in the center of one wall to avoid having a "boomy" bass.
