It's a mallard, you won't be able to know the gender for a few more months. Give him waterfowl starter, from your local feed store, but if they don't have it get chick starter (18-20% protein) and plenty of water. I also suggest getting vitamins and electrolytes (also at the feed store) and...
If he already can't hardly walk, he's probably dying from his weight. His legs can't support his own body anymore, and it's overloading his heart; this happens often with meat breeds. They aren't mean to live longer than when they'll be sent to market, to be honest. I'm really sorry, but there's...
Definitely not a rooster. She more than likely just hasn't started her cycle yet, like hitting puberty late, she should be soon especially since you've got rubber eggs. She's just slow to mature.
It shouldn't cause them any harm, I'd really hope what I put in my food is safe enough not to harm a chicken's feathers. Some people will be judgmental about it saying it's unnatural but don't let it bother you. If you do, post the photos!
Some chickens just do that, and the others are following their example except only the bantams are light enough to actually be able to stay on the branch.
Do you have a lot of predators in your area? If not I wouldn't worry about it a lot but you might want to confine them to the coop for a...
How old are they now? I'd get all of them down with the help of friends/family and confine them there for about two weeks to make them sure they know this is where their "home" is, and then see if they can adjust their behavior after being let out again. It seems cruel but it would be more...
Maybe you could try a dual-purpose breed if you're looking for a more attractive option that's better than free-ranging?
I've noticed with Cornish X, everyone seems to get different results, I had some and despite having a ton of room and grass, they refused it even having been exposed to it...
That's really odd, maybe she has abnormal ovaries or hormone issues? If she's not having any health issues I suppose it's not an issue but I'd give her extra calcium, like crushed egg shells or oyster shells. She's very young so I'm sure it will take a lot from her.
My red-sex link did this also when she first started laying, and then it evened out, so I wouldn't worry unless it doesn't stop.Try giving more calcium and feeding egg shells back to her (crushed finely of course)
They are probably frustrated from lack of stimulation in the run. Do they eat any treats other than layer mash? Are they allowed outside of the run? If so, they may just be having pecking order issues, but if not, it's more than likely due to boredom and I'd recommend letting them roam for a few...