I would also wait 4 more weeks before letting them have physical contact. In a small cage as introduction is fine now, but they need to be large enough to defend themselves, 4 weeks should do that. Good luck!
And oh, there will be fights, squabbles, and probably a few bloody combs. However, tough love, unless someone is really injured beyond a comb bleeding, do not intervene. I see lots of people feeling bad and taking hens out all the time and have a three month journey in integration. Once they are the same physical size and eat the same food, let them dual it out with places for the youngins to hide if necessary. Don't want the older ones to learn that beating on the chicks makes the big chicken *the human* take out the "intruders".