I'm not sure about the panel traps questions, I'd better leave that to Ethan.
>3.Since I cannot mount fiberglass traps on the wall, will they work if suspended using wire from the ceiling a few inches away from the walls? (would sway if pushed)?<
Actually, they would work better, if you can spare the room. The added air space behind the fiberglass will make them absorb to lower frequencies as well as higher. But for actual rigid fiberglass bass traps, those would be best placed straddling the corners of the room, from floor to ceiling if possible.
>4. I am quite curious to what effects overdampening would have on a room? Does music really sound weird or 'dead' in an anechoic environment? Since I am also using the room for playing electric guitar, and jamming, I assume the more dampening the better. Am I correct?<
Yes, music sounds dead in an anechoic environment. If you have a walk in closet filled with blankets and other such soft materials, play guitar in it for a minute and it may give you some idea. It basically sounds like playing in a vacuum, if you can wrap your mind around that.
As far as whether or not it would be good as a recording environment, that's more a matter of taste. A well treated live room can sound really amazing. But if you're using this one room for recording AND mixing, I'd probably advise making it more dead than live.
The reason for this is that while a 'live' sound can work great for recording, you want a more dead room for mixing. If you mix in a live sounding room it can give you wrong impressions of how much room there actually is on the recording because you may have trouble telling what's the recording and what's the listening room.
If you make your room more dead, you can always add reverb later (I know, it's not the same, but we who are on a budget gotta do what we gotta do).