Hi, and welcome!
For starters, I wish we were all lucky enough to start with a dedicated room! Okay, lets start in on the questions. If you carpet everything, you're going to have a VERY dead room. But it will not fix bass issues. Ethan Winer posts here frequently, and he has a lot of knowledge on acoustics and bass traps and such.
Question: What is your overall budget at this point, and what equipment are you starting with?
As for the component and screen wall, I think you're going to want more than 2' in. Since I assume you're going to put all your components in a rack, then that's 19" by itself. If you ever plan on making an access to the area behind this wall, then you're going to want more room back there.
I assume that at one point you're going to want inwall speakers, perhaps something sexy like
this at some point. Since your current speakers are NOT designed to be in-wall, you might want to leave them out for right now. If they are a sealed or front ported design, then you might have some luck recessing them. Otherwise, you're going to have issues. Also, they can't be flush to the wall without having high frequency diffraction issues (read: highs will sound like crap). As far as subwoofers go, most in-wall subwoofers I know of have a limited response and won't provide you with couch shaking subsonic bass. You might want to look at getting a velodyne subwoofer (or two!) and mounting them into the wall with some isolation. Since they are a sealed design, they won't have any port issues. If you had the cash, two DD-15 subs would be amazing (though expensive).
Random tip for wiring: conduit is your friend.
Onto the other questions:
1. Use this handy
calculator to figure that stuff out.
2. I honestly don't know what would be best. I'll defer to the acoustics experts.
3. Not sure about the padding, but otherwise a great idea. Do you plan on having a smoked glass door for the components, or will that be completely hidden and have a separate access? If you're going for a door, then something like
this or
this. Obviously you might want to install some quiet fan panels to help keep everything cool and happy.
4. See what I said above.
This sounds like a great project, I hope this helps!