Please be sure and read the pinned topics. You'll find at least 3 that cover your questions fully. There's one on
why you need a fry tank sooner rather than later, as well as one on
what's bad about breeding traps. And there's yet another on
caring for baby livebearers generally.
Looking after baby mollies is quite straightforward. Mollies need lots of space if you want them to develop properly. This is especially true with sailfin mollies. Adding some salt will help, too (around 3-5 grammes per litre of marine salt mix). Yes, you can keep mollies without salt, but your life is so much easier if you use salt. Mollies MUST have access to algae; use a good "vegetarian" flake food (your LFS will have some, it's very widely used by livebearer and cichlid keepers).
Your baby mollies will likely need to be removed from the trap/net to another tank within a week or two. Once in the raising tank, they will be there for about 3 months before they are safe enough to mix with potentially predatory tankmates such as angelfish or large tetras.
As far as moving fishes go, don't worry about it. The secret is to keep the fish in a covered container with plenty of air. Given it is summer now, overheating is more of an issue than chilling. I would go to a DIY or hardware store and buy a bucket with a lid. These cost very little, so buy several: you can never have too many buckets! I use 10 gallon buckets, which cost about 5 UKP. Err on putting too few fish per bucket. In a 10 gallon bucket 1/5 filled with water, I'd keep around a dozen molly sized fish and expect them to be safe for 6-8 hours, at least. Fewer fish would mean the water would be fine for longer, so adjust the stocking to match the length of travel. Resist the temptation to keep opening the buckets to check on the fish. Keep the fish somewhere dark, not too warm, and above all quiet. If you can, cover the buckets with a blanket to keep the fish dark and sleepy.
Cheers,
Neale
Thanks!
