If you've gotten the class, you also unlocked the shop selling the equipment you need if I remember right.
Which item, I'm pretty sure the Cat has a 'damage' type weakness listed if I remember right.
Topaz is an Event (Like the Night Hunt you see mentioned) specific gem. It's unlocked at the same time you unlock events.
Gathered the same as normal gems once unlocked, UNLESS there is a 'Large' Event (Like Night Hunt) active.
Potato Water is a 'Fertilizer' item. Not able to see what it does, or how much you have, until you unlock the feature. Can still gather up some ahead of time though.