There is no reason to feed f/t in a different bin or tub. Feed the snake in its home and you will reduce stress on the snake and you. Cage aggression is a myth and moving a snake in feed mode only increases your odds of getting tagged. Don't believe me then do a search here and see what the more advanced keepers do.

As far as the shed the belly should be getting pink or be pink if a shed is just beginning. It should be pink before the eyes get foggy. After it gets pink then the snake will enter the blue phase and get the cloudy look to it. Then that will clear and the snake will shed a short time later.

I never refreeze a rat that has been thawed longer than an hour. The rat you have should be tossed. I thaw mine in water because it is much faster and better than having 8-10 rats sitting around thawing out. I don't think the wife would like that. When they are thawed and warmed properly I use tongs to dangle the rats into the snakes cage.