First, I think you are overfeeding.
I know the fish food bottles usually give the instructions of feeding 2~3 times a day with each meal last for 2 minutes. They certainly hope you can go through the bottle as quick as you can. The truth is, there is no problem at all if you just feed once a day or every other day. A lot of problems are caused by overfeeding.
Second, do you have any sharp objects in the fish tank? Sometimes these objects can tear or injury the fish. Remove them immediately if you have any such objects in your tank.
Third, you don't have to separate these fish permanently even if they have been in fights. Do you have a large bucket? Take some tank water into it, and move the bully fish into the bucket. Let him/her stay there for an hour or two before return him to the fish tank, that will teach him/her! LOL. Seriously, it has been shown as a working tactics against the bully fish.
