Sure, he could if he wanted to. However, it is important to remember that even though everyone's actions are meaningless in the big picture, they matter to the characters themselves.

It would depend on how it was done. Sometimes having the bad guys win can make for a marvelous ending.

First of all, I have to do nothing of the sort. Secondly the "paradoxical universe" that I was talking about is the same as the "real" one that you are talking about. It is also still just the figment of someone's (in this case, Robert Jordan's) imagination.

Science is a philosophy, but philosophy is more than science. Philosophy is the study of thought.

Also, you're wrong. Rand is ta'veren. The Pattern spun him out for a purpose, and it gives him what he needs to accomplish that purpose. It gave him Moiraine, and yes, she helped him. A little anyway, at first.

If she hadn't been there, someone else would have picked up the slack, and Rand still would have been fine. You have argued that that argument is invalid; that even if someone else could have done what Moiraine did, she is the one who actually did it. By this logic, Master Hightower is one of the most important people in the fight against the Shadow. He took everyone on the first ferry trip as you will recall. Without him, Rand and Moiraine and everyone else never would have made it out of the Two Rivers. Pretty silly huh?

I also need to point out that in every book except the Eye of the World, Moiraine's plans and goals are just plain wrong, and more often than not would play directly into the Dark One's hands. For the vast majority of the series, Rand succeeds in spite of Moiraine, not because of her.