I seem to have issues using the game's voice chat -- it's not clear, and slightly laggy -- and I would rather have something just running all the time as I play... Is there a recommended outside voice/game communication that myself and my friends could run? Is something like that even allowed?
Yes, you can use outside ones and should as they are superior in every way (though some you have to pay for or host yourself), big ones being Ventrilo, Team Speak, Mumble, probably others
