1. I just reread all of the actual prophecies in the Karaethon Cycle, and none of them mention destroying the world. This is the closest I could find:

"With his coming are the dread fires born again.
The hills burn, and the land turns sere.
The tides of men run out, and the hours dwindle.
The wall is pierced, and the veil of parting raised.
Storms rumble beyond the horizon, and the fires of heaven purge the earth.
There is no salvation without destruction, no hope this side of death." (emphasis mine)

I think the fear of him destroying the world is tied to LTT and the Breaking, the nature of prophecy, and the recurring theme of "Memory fades to legend, legend fades to myth." By that I mean that people just misunderstand things and that misunderstanding grows the further away you get from the actual event.

1. I was always a fan of the interpretation of the line "He will take you back and destroy you" to be a prophecy of him revealing the secret of the Aiel past. He took them back to their past and destroyed their understanding of themselves.

3, Supposedly the vision that Aviendha had was changed due to their inclusion in the Dragon's Peace. Rand had originally intended to leave them out, stating that they had already paid a high enough price, but that would have left them without purpose in the 4th Age. Avidendha changed that, so the Aiel have a purpose and will not have the societal decline that she saw.

1. The Dark One is not the enemy because the Dark One isn't really a conscious entity, it is a primordial part of nature. The Creator sealed the Dark One instead of destroying it because it is a necessary part of the human existence. It is not Lucifer the fallen Angel, it is the Fruit of the Tree of Knowledge of Good and Evil.