The simple solution to feeding a mixed age flock is to feed them all the same thing, Starter, Grower, Flock Raiser, or something else fairly low in calcium and offer oyster shell on the side. The ones that need it for the egg shell should eat it and the others should not eat enough to harm them. Don't freak out if you see the young ones eating a bit. They might experiment with it, but they should not at enough to harm themselves.
The integration question is a lot harder. I integrate 8 week old chicks all the time without serious issues. I have broodies that raise chicks with the flock and wean them anywhere from 3 weeks of age to 9 weeks. I have a lot of space. I think that is why I don't have serious issues.
Mature chickens will always outrank immature chickens until they mature. Then they will find their place in the pecking order. What normally happens is that a mature chicken will peck an immature chicken if it invades her personal space. The younger chicken runs away. All is well in the chicken world.
But if that younger chicken does not run away, it is a challenge to the pecking order. A serious fight can ensue. Usually these end pretty quickly in some chasing and running away, but occasionally they get serious. If your space is tight where the younger chicken cannot run away, the danger level goes way up. That's why space is important. You are going to see some pecking, chasing, and running away. That is normal. You don't want it to get bloody.
Normally you will see the younger chickens acting like a totally separate flock. They try to keep a distance between themselves and the older ones. This reduces the chances of conflict tremendously. It also helps to have separate feeding and watering stations so they can eat without challenging the older ones.
It helps a lot to house them side by side for a while, where they can see each other but not be able to attack each other. That way, they get used to those chicks being a part of the flock. It does not solve the pecking order issues but it does help a lot in just basic integration.
Sometimes these integrations go really smoothly and you wonder what all the worry was about. Sometimes it gets really messy.