Scratch can be good for boredom, throw it in the run to give them stuff to scratch for, but you're right it can lower protein, I like keeping my hens on a grower or an all flock because it has higher protein, I also give mine some black oil sunflower seeds, I have had good luck doing deep litter in my run, we put grass clippings, fall leaves, garden produce, and I like bales of hay, they scratch around and eat the grasses and it encourages good bugs in the soil.
I would toss them food scraps in the run when you have them to keep them busy, I would put logs and perhaps some perches for them to get up on.
You are right about the rooster leaving messes with the pecking order, as well as roosters will break up hen fights. They are at a goofy age where they aren't mature mentally, in a normal flock there would be roosters and older hens to put them in their place. They should eventually calm down and maybe by then the hen that was pecked on can rejoin them, and if you can identify the leader in the pecking she could spend some time in jail to knock her down a bit on the pecking order.