No to both.
For cards that place microbes/animals on another card, doing so is never a requirement. Only cards that use microbes/animals (either for an action or for VPs) can store them.
to precise, you could place a microbe ressource on a card without "microbe" tag, so long as the card has a use for those microbes.
I don't recall if all microbe using cards have microbe tag, but the case could exist.