think about it. all the other avatars tried to kill whoever was trying to take over the world. Aang however doesn't kill firelord roku (or whatever his name was) that was trying to take over the world, instead he took away his bending and because of that the world could finally live in peace.

This applies to much more than just the Avatars - Aang was the only person who couldhave saved the world. If anyone else - Iroh or the OWL, the rest of the gaang, etc, had dpne the job it wouldn't have worked out. People would have seen it as just one more death in an endless war. Aang however, was the only person who could finish the war on the right terms. Peaceful terms.

Ahahaha. VICTORY!

Well, it was kind of implied that Aang's resistance to violence and his solution the world would help prevent war for a very long time. Technically the previous Avatars didn't save the world, they just postponed the war. Aang ended the war. At least, as I said, it was implied.

This is a moot topic. Had it been an Avatar aside from Aang, the world would not have progressed into that state.

Avatar Roku spared Firelord Sozin, and look what that got the world into.

Chin the Conqueror died against Kyoshi, albeit accidentally, and an era of peace started.

Judging from this past failure and past success, the Avatars were quite well-founded in recommending that Aang kill Fire Lord Ozai.

What would have happened if Aang had killed Ozai? No, the world would not have stayed in violence- Iroh stated as much. Axrendale, yes, Iroh said if he himself had killed Ozai, then the world would view it as more senseless violence, "a brother killng a brother to seize power". But that didn't mean the Avatar couldn't do the deed. Really, the pros and cons more heavily favor what would have happened if Ozai had died rather than been killed.

Killing Ozai

Pros:
No more threat from Ozai in combat.
The Fire Nation is no longer lead by Ozai.
Ozai cannot return.

Cons:
People will be angry about the slaying of their leader.

Stripping Ozai's power and locking him up.

Pros:
No more threat from Ozai in combat.
The Fire Nation is no longer led by Ozai.

Cons:
People will be angry about the imprisonment of their leader.
People will pity with him- he's the only person in recorded history to lose his bending.
Ozai will be able to return, organize, and lead forces.

As you can see, killing him had all the pros of locking him up, but less cons. Letting him live was an acceptable option. But that neither means it was the only acceptable option, nor the best option.

she could be of good use in the "new world order" that Zuko and Aang have established. The Fire Princess Azula. and she'd be a good one. if she was good, she'd be a threatning force in the evil that resides in the avatar world.

I don't think that Azula will ever become an outright hero. Rather, my best guess as to what would happen if she managed to heal her insanity and somehow find redemption is that she would eventually become an Iroh-like character. It would be interesting if she joined the White Lotus - she strikes me as the type of person who would pwn at strategy based board games.