When does Nyn pass this info on? I was under the impression it was after they had left. She doesn't. I think Morraine just suspected she was not telling the truth. I don't think she had much experience lying.

Mordeth/fain have nothing to do with the ways and the black wind. The black wind is Masadar. Fain becomes machin sin. He has nothing to do with the ways. By the end fain IS machin sin.

dislike to like Mat Galad liked for the whole series Moraine Tuon Perrin Faile Rand Thom Land Egwene Gawyn Tam al'Thor Logain Nynaeve

I like Gawyn. He saves Egwene and you know that he truly does love her because when Egwene bonds him it tells you how she can feel his love.

I don't think the books would be half as fun and exiting if Mat was not a main character.