Quite frankly, she is the one Forsaken who has been totally upfront about her overall interest in him and I can understand her, because I would most likely be the same way. She has no interest in him because she was too busy trying to A) survive and B) become Nae'blis. I seriously think her strategy didn't involve him, and she basically had a hands off approach allowing Moghedien, Mesaana, Rahvin, Demandred, Sammael, Lanfear and Ishamael/Moridin to get winnowed out trying to capture or turn him. I think her strategy was to manipulate the particular Forsaken who was trying to capture Rand - not capture or manipulate Rand directly. This is why I believe she manipulated events to plan her escape while removing as many traces of her trail as possible.

Personally, I think Rand is the prime candidate for the source of those voices because it seems to be his inherent personality to have these drives, and all Tam's guidance did was establish a moral system that seems to have been in conflict with these drives. It says a lot to me that Rand was essentially a passive personality and as soon as he needed to get aggressive and fight, he had to develop a switch. Lews Therin, IMHO, also had a very aggressive (ie: annoying) and narcissistic personality so it seems to make sense to me that Rand's personality might have been the same, since a soul may very well carry the nuggets of your personality into the next life.