It looks like the v6 can connect with all Tama Connection versions. In the connection menu, there's a choice between connecting with "Music Stars", or "Others". When connecting with v5, the Tamas will play their usual games (but the v5's sound chip has a higher pitch than the v6... when they play the piano game together, it might hurt your brain). You can even sent one of your v5 Tamas away for marriage, although it'll appear as that weird black Tama with the hat (the one that brings you your mail occasionally in v6). I also read that you can develop friend points like usual with the other versions, and that they'll marry when the hearts get high enough.
I believe the v6 will adapt to the games of whatever version it connects to, although I've yet to test it since my v1 is out of batteries (and Lucky's hasn't restocked in a week).