Hannaransom, could you post some good pics of these chickens?
The space you describe in your coop and run may sound adequate for the number of birds you have now, but will be pretty cramped when your other young ones get bigger....even with free ranging. Unless your coop has really great ventilation(like two whole walls of it) and multiple places of their being, it's going to be hot and crowded at night and the total area is going to be too small if the birds have to be confined to run and coop for any length of time for some reason....just something to consider here.
As for integration, I'd rig a place where the younger ones can escape the older ones if they are to remain confined to the run and coop....a pallet of some kind up on blocks is helpful or even placing a temporary wire fence with a gap at the bottom just high enough for the little ones to go under while out in the run. Having their own small feeder and waterer in that area will help keep them from getting the worst of community living.
If free ranging at the time of integration, they should be able to escape any trouble from the older hens and should be able to fend for themselves at the feeder after the older hens are done eating.
They really don't need to be wet down if they have adequate shade, plenty of water and plenty of open ventilation.
Some good pics of your yard, coop and run may help folks give you more or better advice on this matter.
Anyone else have anything they want to add to this? My experience with flock integration of different aged birds is limited to free ranging and not geared towards smaller confined areas, so others with more experience in that area may have much better ideas..