Chickens really get stuck in habits. Until they accept the new coop as home the hens will want to go back to the old coop to lay eggs. The flock will want to go to their old coop to roost. If you have room, I suggest you lock the flock in the coop section alone for a few days, maybe up to a week. That way they will come to accept the new coop as home and roost there. The hens will learn to lay in the new coop. Then you can let them in the run.
Chickens can fly over a 6' high fence, even the big breeds. It's a matter of motivation. I don't have any trouble keeping chickens in 4' high electric netting, yet I have seen them clear a 4' high fence easily when something causes them to want to, like a hen wanting to get away from an amorous rooster. They can fly really high to get to a roost. How much space they have to get away from each other makes a big difference.
Something else that can happen. If you have a top rail on the fence, chickens may fly up there just to perch. Once they are up there, they may hop down either side. Once they are out, they don't know how to get back in. If you don't have something on top of the fence for them to perch on, this does not happen. The tops of my fences for chickens are wire, not anything that looks like they could land on like a 2x4 or metal rail.
Each of us have different set-ups and conditions. Each flock has its own dynamics. I can't tell you if yours will want to get out or not. Normally I'd think a 6' high fence will work well, especailly if it does not come with a perch on top, but leave them in that coop for a few days to reduce their motivation to go lay an egg or roost in the old coop.
You can clip a wing if you want. I don't know if it is necessary or not in your specific unique circumstances, but it really, really won't hurt them. There is something up in the Learning Center at the top of this page that shows you what to cut. Wing clipping may help keep them in until they get used to their new quarters.
Good luck!
