For food, it should be safe to feed grower feed to all of them, young and old. Just make sure there is a dish of oyster shell so the laying hens can get the calcium they need. (The hens will usually eat the right amount, and the chicks will usually take a taste and then ignore it until they are old enough to need it.)
For integrating them, you can probably start now, by arranging for the chicks to live near the adult birds, separated only by some wire mesh.
That way they can all start to get to know each other, and no-one will get hurt.
After a while, you can start letting them spend time together (supervised). When you actually combine them, it helps to have lots of space in the pen, more than one feeder & waterer, and some places for them to hide or get out of sight of each other. Bales of straw, or boards leaned against the fence, are possibilities for "hiding" places. You want the chicks to be able to run behind something or into a space, but they need to be able to run out the other end so the big birds cannot trap them in a corner.
Some people set up a brooder in the coop, so the chicks and adults are getting used to each other from the very first day.
Here is an article about how one person does it:
https://www.backyardchickens.com/articles/my-coop-brooder-and-integration.74591/
Since your chicks are already 6 weeks old, they may be too big for the idea of chick-sized doors that large chickens cannot go through (in that article), but it's something to keep in mind for future years.