Aged Copper takes a really long time to dry--I'd give it 5-6 days before you clear coat it. I've noticed that 3 colors from the Universal line are all slow to cure, and you can dent them even after 2-3 days. If you clear coat such slow drying paint too fast, you risk the bottom layers not fully curing in some places, because clear coats normally dry quickly and are quite hard. Which is why I recommend waiting for that particular paint.
Don't wet-sand between coats--just after you've finished all the color coats or color + clear. You don't really need to sand it unless you want as smooth a surface as possible, but remember that by sanding flake / metallic paint like that, you'll be changing its appearance a bit. It will look more silver where you sanded, as more of the paint will be removed and metal flakes will remain. At least that's been my experience. I would let that particular paint cure well for 5+ days and then do 2-3 layers of clear gloss. Then couple days later you can wet-sand (2000-grit) + polish that.
Regarding dust / fibers... yeah, those are terribly annoying, and that's the price we pay for not using proper painting booths. Not much you can do other than let the paint dry and try to rub them off with a bit of paper towel. You don't want to touch the surface with your fingers much, as that will introduce oils and dirt, and you'll be clear-coating it. You can scuff the surface lightly with wet 2000-grit sandpaper, rinse off REALLY well, buff with a soft paper towel or microfiber towels, use something to blow all the dust away from the surface (like a can of compressed air), then clear-coat.
Oh and wash your hands with soap and dry them very well before handing prepped and painted pieces.