While training can a hero learn a skill that he doesn't have power die for? For example in my current Advanced Campaign I am Grey Ker , he has no starting skills or power die in fighting. Would he be able to learn a fighting skill during the campaign?

Thanks.

nuzreq said:

Yes.

There is no such requirement written in to RtL.
I think it has been explicitly clarified somewhere (GLoAQ?), but even without the clarification that is the way it was if you follow the RAW.

Yep.

The skills on the sheet are only for starting skills and all Feats (if you have ToI). You can learn whatever you want, as long as you go to the right town and/or secret trainer.