What size are your hens? That applies to both questions. Cats are predators, but they are pretty much cowards. They tend to tackle only prey smaller than themselves, often quite a bit smaller. Songbirds are certainly at risk. Baby chicks are at risk. But unless you have some pretty small chicken breeds or have some really large cats, adult chickens are not likely to be at much if any risk. You are dealing with living animals and each one is different so I can’t give guarantees, but domestic cats are not high at all on my predator worry list.
Can your chickens get out of a 6’ high fence? I don’t know your breeds. Some fly better than others. Silkies can’t fly at all. Some other decorative birds may have trouble flying. But bantams fly better than Games. Games fly better than the full-sized breeds and games can usually fly up to a fifteen foot high tree branch to roost if they want to. Practically any chicken can get over a 6’ high fence if they want to. That’s with their wings not clipped. When you clip one wing you limit that mobility a lot, but they can still jump/fly better than some people expect.
A lot of that is motivation. Chickens don’t always escape fences by just flying over them. They can reach pretty great heights by using their feet as they flap their wings if properly motivated, pretty much climbing the fence instead of flying up and over. Where I’ve seen this is when a hen is trying to get away from an amorous rooster or a chicken is trying to get away after a pecking order or flock dominance fight. These fights sometimes end with running away and chasing. I’ve seen chickens reach amazing heights when they are trying to run away but get trapped against a fence. I don’t clip my chickens’ wings but from what I’ve seen I would not expect that to slow down a properly motivated chicken that much if they really wanted out. They just flap and walk up a fence.
With all that said, I keep my chickens inside a 4’ high electric netting and they hardly ever escape. When they do it’s generally juveniles with their dominance/pecking order fights at blame. They have a large area to roam so they don’t have much motivation to get out. I saw a full sized hen fly over that netting and clear it effortlessly by a foot when I carelessly left a door open and she got out. I trapped her against the netting to try to catch her so she just launched and easily few over. But the adults never just fly out. So there is a good chance yours won’t even want to get out even if they could.
Clipping one wing will stop them from casually flying though. It throws their body off-balance so it’s more uncomfortable to fly. It also reduces lift. It does not prevent them from flying or in many cases jump/fly to reach heights. It restricts how high they can go and makes it uncomfortable for them to even try. It can be very effective.
Something Aart referred to. Chickens like to perch. They will jump/fly up to a perch just to look around and enjoy the world. They seem to get a lot of pleasure out of that. If your fence has a solid top that looks like a good place to land, they may want to get up there just to perch. Once they are up there they may hop down on either side. Once they are out they generally don’t know to get back in the same way they got out. That’s where a wire or some type of top that is not a good place to land is a strong deterrent to them flying up there.
Will your hens reach the fence if you let them out? A lot of that comes down to motivation, whether the wings are clipped or not. From what you describe I’d be quite willing to try it with or without wing clipping, but a fence with a solid top would concern me some.
Good luck!