Pft, Live Bait? Admin abuse? No xD, what I think happened is this:
On your first ban you were banned by Pyro, for teamkilling, Pyro's always been a good admin for hidden from what I recall so it's likely he banned your for a reason.
Second ban, teamkilling, by Wooley. This one, as I saw earlier from your previous ban appeal/admin abuse thread is likely bogus.
Third ban, by Live Bait, for teamkilling. It is possible that you were caught up with the teamkilling of your friends and consequently banned for it, without you perhaps participating. Assuming that Wooley's ban was bogus, which in all likelihood it was, that leaves you at 2 bans for teamkilling. For now, we'll have to wait and see if your ban was warranted by having Inject get the server logs for the general time you were playing and checking whether or not you actually teamkilled.
The reason you were permabanned is because, in CG, players on the hidden servers are permabanned after their third teamkill offense. Live was just following proper protocol for banning players on their third offense.
Hacking:
As for your friend hacking, Live always records demos of hackers, so hopefully he has a recording that seems to show your friend hacking so he can prove what it was that made him think your friend was hacking. We'll have to wait on him for this.
@Edit: Your friend has been banned twice for hacking via mat_fullbright -_^ so that already shows he is fully capable of using hacks and is willing to do so:
http://hidden.universaldings.de/sourcebans/index.php?p=banlist&searchText=STEAM_0%3A0%3A40088242&Submit=http://bans.ptga.me/index.php?p=banlist&searchText=STEAM_0%3A0%3A40088242&Submit=It also appears that banning for mat_fullbright on CG isn't working, for some reason, which would allow that hack to be used easily.
-_^ and finally this, if anything these should have been a ban appeal, not an admin abuse thread. Live probably had some very good reasons for banning you for teamkilling and your friend for hacking. Everyone can be wrong though, so perhaps you weren't actually a teamkiller and perhaps your friend wasn't hacking. Either way, it wasn't due to Live being an abusive admin, it's either due to a mistake or you and your friend actually doing something both of your shouldn't have been doing.