Zitanix, thanks for bringing all of these concerns up - you've demonstrated a lot of thought!

I'll try to address each problem you've listed.
First, everyone needs to have a teammate chosen before the tournament starts. If not, a lot of people won't actually be able to participate, and that would suck for everyone.
This is actually the least of my concerns. My reasoning is that we all are pretty well familiarized with each other - I doubt anyone would have
too much trouble just PMing someone and forming a team. Then again, I'd be sad if someone had to endure 'picked-last-itis.' I'm just hoping that people will be nice about this process, and not be like: "No, you can't be on my team because
u r teh sux."
Secondly, the matches would require a bit of communication between teammates. You need to be on the same color team as your partner, (I think) everyone needs team attack on or off depending on the rules, and if partners want to change characters during a set, they'll need to communicate on AIM or something.
The color issue would be easy enough for me to assign. Say, if you're on the top of the bracket, be red. On the bottom, be blue. Also, the rules could be assigned. Communication is somewhat of a problem, but I think with all of the chat clients and skype running around, it wouldn't be too bad.
Third, all four players would need to agree on a time, and that could potentially slow down the progress of the tournament.
I hadn't thought of this. However, given that the team tourney will likely have roughly half of the entrants (teams versus individuals), it would obviously get done faster. So, maybe give the time of two rounds of individual play for every round of team play (something like that?).
My biggest concern is still lag. I know there are certain people around here with blazing internet speeds. I'm not so fortunate, so every time I host a FFA, it lags. It eventually gets better, but it still lags. Shall we all just agree to saddle up and endure any lag?
Hmm, I still wonder whether it is wise or not to conduct two tourneys at the same time. The scheduling will obviously conflict.