What do you think happened with Cadsuan and that wilder(Norla?) back when Cad was young?

Cad was fresh to the shawl and was one of the most powerful Aes Sedai in centuries so she thought she was all that and a bag of potato chips.... Not that she doesn't think that now.

 

Anyway she ran across Norla in the Black Hills.  I imagine there was some confrontation between the two where Cad was being the overbearing Aes Sedai we've all come to know when Norla then beat the stuffing out of her (figuratively of course).  I think of it similar to how the Wise Ones disabused the Aes Sedai put under the care that they were the best at everything.

 

Anyway the impression she gave was that she received additional training from Norla, and as rewards Norla began giving her the Ter'angreal that she carries today.  She makes the comment that if she hadn't gone out into the world then she never would have met Norla, and she [Cad] would probably be dead now.... I assume this is a reference to the Ter'angreal saving her life over the years.

might also include advice on how to deal with men

Did Cadsuane swear at some point that she'd not die til the Dragon was Reborn?