Oh, they're young ones... yep, almost certainly pecking order.
Yes, you can feed starter (well.. actually, you probably want to find some "chick grower" now... it's a little lower in protein and probably is just a bit cheaper. Also, if the starter is medicated, you don't need that any longer... and you want them off any medicated feeds for a bit before they start laying.)
When they'll start depends to a great extent on their breed, and seasonal issues.. but you shouldn't have the "seasonal issues" stuff because of when they were hatched. Most "laying breeds" (ie; leghorns, and other smaller white egg- layers) start laying at around 4 1/2 months.... 18 weeks. Heavy breeds- the brown egg layers- tend to take 2-6 weeks longer to start. It's individual, as well... some mature quicker than others.
You can feed scratch at any time... make sure if you do they either can get outside or you feed grit (necessary for them to be able to grind whole grains in their crops).
Nests should be ready for them to use by the time they're 16 weeks or so. You only need one nest for every 4-6 birds... but even if you provide 1 nest for every hen, you'll find that they choose one or two and EVERYONE lays in those. Even to the extent where you may find 4 hens in the same one, at the same time! LOL!
Roosters... you don't NEED one. They serve no useful purpose if you don't intend to hatch eggs. They're one more mouth to feed, and they tend to be noisy. On the other hand, they can be "insurance" that you would have fertile eggs to hatch in the event you couldn't simply mail order new ones, and they tend to be protective... although not always effective, they will try to protect the hens.
(I'll add that if you have small children, roosters can be dangerous. An aggressive one can fly right in the face of a toddler or preschooler. Something to consider)
Now, if any of them are getting pecked to the point where they are injured, that needs to be stopped. Sometimes you can stop most picking (cannibalism) by providing a little more protein... if you're not squeamish, road kill (yeah, I know... yuck!) is actually darned good chicken feed. Some folks swear by adding a bit of apple cider vinegar in their water... maybe 1 tablespoon per gallon.
There are products with pine tar in them which you can smear on any actual injuries (or any spots which are so bare that if they keep pecking, they will break the skin). It apparently looks like blood to the other birds, and tastes terrible.
You can also simply snip a tiny bit of the upper beak off... use heavy human nail clippers or those "nail scissors" they sell for heavy toe-nails. You are just blunting it... but it helps keep them from grabbing skin in their beaks and basically pinching some flesh off. I've had to do this with a couple batches of Cornish-cross birds, which I know were more crowded than I like to keep them. Birds which aren't crowded, not overheated and have some access to the outdoors (in other words, aren't bored out of their tiny skulls) tend to not peck much. However, they do establish that pecking order, no matter if you've got the Chicken Shangri-La there!
Only you can decide if you want/need to try hatching chicks. Depending on what breed(s) you have, you may need an incubator. Some breeds are inherently broody (Fred's Buff Orpingtons, for example), and occasionally you'll get a broody hen from a breed which is considered "non-setter" (which means basically that they bred the broody instinct out of them). I had a Golden Comet hen (which is a sex linked production hybrid- they are most definitely supposed to be non-setters) sneak out and raise two broods per summer up in our haymow, every year for 4 years. Someone forgot to tell HER she was a "non-setter"!!
Questions are fine... all of us had to learn sometime. I can laugh now at how many times I went back to some of my basic books at first, about 20 years ago. Don't hesitate to ask... someone here will probably have the answer!
Summerthyme