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I dont think she is TOO thin, just feed some protein rich, quality, live foods regularly along with your staple for a while to get her conditioned up.
Of course, never over feed. Add just as much as your fish can eat and when she is conditioned up use your live food less often. it can give them fatty livers and such and harm your fish.
Bad idea! Breeding cages (usually called 'traps' for obvious reasons) are not large enough and will stress you fish more than being in an aquarium. A small tank (2½ gal./10 l or larger) would be much better. Small tanks are ideal for this as well as using as a quarantine/hospital tank.