firewalls do not cause problems, if anything its app setting, or maybe you need to give the app permission to pass through the firewall. Anything that has the potential to link with various unknown sources is a possible danger to the pc. I tried teamspeak once for some reason I cant recall I did not like whatever it was doing so quickly binned it.
your AV wont pick anything up until the software is active, if it picks up anything at all. It would have warned you when you were downloading/installing if anything was there. As TS is an internet programme I would think it would need to be live first.
I use AVG Internet Suite 2015, it has not been beaten yet.