What is this slimy coloured stuff growing in my plates?
My first guess is oil deposits that have hardened through oxidation. Especially the highly unsaturated oils are prone to oxidation, which will after a while lead to insoluble deposits (like in the original oil paints, where the linseed oil polymerises after prolonged contact with air). It's hard to remove as it's not brittle, and deforms rather than breaking, like an oil varnish.

(are those items you show plates, or pan covers/lids?)

It doesn't look like any kind of mold.