Mold and pop-up drains
Does this mean my drain has been malfunctioning for some time?
No, a malfunctioning drain does not cause mold by itself.

How can I prevent this from growing back?
If it is so important to you, you can disassemble the drain parts twice a month and clean them with bleach, but that stuff you think is mold is actually a mix of soap scum, toothpaste, lotions, decomposed organic matter, bacteria, etc. and is in every sink drain in the world.

Would it also be safe to assume that my emergency outflow channel is super moldy as well?
Very likely.