Short answer: no, it is unlikely. There are some concerns with eating potatoes, but these apply to any form of consumption of them.
Maybe. The main risk from potatoes (along with most garden plants) is ingestion of pesticides, fertilizers etc added to the garden where they were grown. So long as the with-holding periods are observed for these ...
I suppose, the reason why the cod got brown, was that after storing the several pieces, the cut face, despite dry and salted, was not covered by the skin of the fish anymore and started to oxidation, hence the brown color.