It's been a while since I watched Avatar, also I haven't read the comics so my knowledge is limited to the tv show.
Round: 1
Azula vs Zuko is naturally happening...While Zuko vs Azula would be a fairly even fight, I think Zuko admitted that Azula is usually stronger than him, he was only confident about beating due to her mental state getting worse. However, I believe end of series Toph and Katara would absolutely stomp Tylee and immobilize her (she has already done that in S2) before she even get's close, . So they'd end the fight quickly before Zuko loses and gang up on Azula.
Round 2: Team Avatar stomps lol. Blood bending can not be countered, add Toph and Zuko on top.....
Round 3: Same result as round 1.
Round 4 : Tough one. With the addition of Mai, whoever fights Ty Lee has to be extremely careful, though I'd say Team Avatar has the better skillset to support each other, like Toph can create platforms, walls and stuff, Katara can use her Kraken technique and both can immobilize their targets also and if Toph is smart she'd go for a rock armor, which makes it impossible for Ty lee to even hit her weak points and for Mai's throwing knifes to injure her. Also iirc, Mai already almost lost to beginning of S2 Katara and Ty Lee had to safe her, so she'd be the weakest of the bunch individually, making her the easiest target.