-Who was the "old Aiel woman" that Rand saw as he was leaving Shayol Ghul? Nakomi?

Presumably.

-What was with Rand producing fire sans the One or True Power? Since he won the Last Battle, did he get to remake reality and so he gave himself supersuper powers?

This is one of the things that Sanderson has said RJ specifically wanted left unanswered.

-Who ordered Slayer to kill Rand? I thought it was Lanfear, but her actions in the end make it seem unlikely. She was going to use Perrin to kill Rand right?

I may be wrong here, but I figured it was Hessalam.

-What was the point of Egwene? She was built up to be this great Amrylin, and then she just dies with no one to witness? Did anyone else even see her anti balefire weave? Will any of her projects like old novices and kin/aiel/seafolk connections even last? I guess Cadsuane will at least have the respect of the Wise Ones (Sorilea)

Egwene was a colossal pain in the *ss, and I say good riddance. However, there WERE witnesses to her death and people know the weave now.

-Now that the Aiel have a purpose, will that change the future of the Seanchan? Or will they always be horrible?

I think it's implied that the Aiel's new purpose averts the future that Avi saw; whether that changes what tremendous dickasauruses the Seanchan are is a different matter. I think that was supposed to be left up to Mat and Min in the outrigger books.