Agree with Paganrose, that's all sound advice.
As for the nest box issue, just because you have 4 boxes for 6 hens doesn't mean they'll be peaceful; I've had over 50 hens all using the same 3 nests and not using all the other nest boxes I made available. What matters most is the chicken's perceptions of the nests. Some nests always look better to them than others. Also, whichever nest has the most eggs is often the most tempting, and whichever nest is highest or most shielded is often the most sought after too. Some hens prefer to lay on the ground.
If you just add more nests it will probably fix the situation, but it's normal for pullets to get rejected from nests hens have been using. Your pullets may never stand up for themselves since they are naturally lower in the order by virtue of being younger. But things should settle down and become peaceful in due time. Might take a little while.
It's a good idea to get false eggs or 'nest eggs' for each nest. When there's always an egg that doesn't get collected, they tend to stop being so anxious about nesting places and sharing; when a hen returns to her nest to add to her clutch and sees another hen sitting in it, if there's a fake egg in another nest it can often tempt her away without her venting her frustration on the other hen.
Some of my hens would forsake cage nests to lay out in the bushes if I totally raided their nests, so a fake egg set we made of plaster of paris proved invaluable. Also it discourages egg eaters if you have any or if they start learning it.
Best wishes.