I'm not sure about Kari, although Moraine knew all of this by the end of the first book, so you don't know...but I think it isn't very likely.

Tam al'Thor was NEVER a warder Tam al'thor left the Two Rivers seeking adventure, and ended up joining the Companions. He rose through the ranks quickly because of his skill with the sword. As for his knowledge about Trollics, he did take part in the battle to protect the Tower from the Aiel, and probably camped with some warders and spoke with them. As for the flame and the void. it turned out that Rand could use it to channel, but it is merely an aid to concentration and could have been taught to him by the man who taught him the sword. As for how he had so much tallent with the sword, that is because he is a descendant of the last kings of Manetheren. The last kind was Aemon al'(something) al'Thorin, and we dont know whether or not he had kids. I think he had a son, named fo his grandfather, Thorin. Thorin had children, and they were al'Thorin al'Aemon, and that became permanantly al'Thorin, which was shortened to al'Thor. It had three thousand years fo this to happen, y'know.

If you recall, in the first book when Tam tells Rand about the Aiel War, Tam states that he brought Rand home to Kari. If Kari was waiting for Tam at home how could she have fought with him in the war?

I think that the theory of Tam being a warder and his wife an Aes Saedai is stretching things a bit. I _do_ think it is likely that Tam was warder trained, but not in the Tower. If an Aes Saedai had remembered the profecies and moved to the Two Rivers to raise a child, it would have been a lot easier for Moraine to track her down. And she or Lan likely would have recognized Tam. It would have made her job of finding the Dragon a whole lot easier. I don't think it was a bad theory, just unlikely.