Clear fins are new fin growth that will take a bit of time to color in. The black stuff could be blue(when bettas are exposed to light their colors tend to go blue), clumped together so it looks black.
If it is black BEFORE it is clear, then it is fin rot.
Edit: If you look at my avatar image...
Ick, that didn't sound fun. I believe you should leave her in the tank rather than stressing her out by placing her into the breeder net. Personally, scooping the fry out after she spawned in the tank saves more fry.
Sorry about your experience :\
Hah, I am in the same boat as you. I have a neon that killed all the others. Now it is fine and fat, most of all thriving.
I guess it isn't that rare ;]
You need 6 shrimp to start a breeding colony. Just let them do their own thing. Provide lots of hiding spaces for the tiny shrimp, after a few molts they will be much like the adult shrimp.