We cannot attack our partner in Team Battle - I had somebody try that at Worlds while I was judging team. They didn't want to flip to use an Eeeeeeek attack so they aimed at their patner.
Correct, you cannot attack your teammate.
Source: WotC Chat (2003-06-12)
In TMP, if I play a Supporter on my opponent...since it's played on him I cannot use any more supporters my turn...but he can use them on his turn correct?
Correct. [Ed. Note: Just for clarification, the supporter action itself must be played during the current turn; it cannot be held over until the opponent's turn. The answer here indicates that the other player may play a Supporter on their turn if they wish.]
Source: WotC Chat (2002-09-19)