Your male seems to have lots of carnucles for his age already. But maybe he's developing them early? It's been a few years since I had any young males to compare with though. They are a good looking bunch.
They like to actually roost. I don't think they will use that shelf as they can't grip it. Some of mine when younger would go 20 feet up into the shed rafters to roost. This hen is about 5 feet off the ground. That seems to be a favorite height.
They must be getting big enough for their heads to stick out the top? The bucket does make it easier.
All that excitement and exercise should help tire out that naughty boy.
If they are in a contained area you should be able to round them up and direct them where you want them with some practice. You could put up a temporary fence if necessary with something cheap like welded wire or chicken wire and some smaller fence posts.
Could be similar to chicks kept in a brooder too long. Sometimes they start harassing each other out of boredom and something to do. I would think you will see improvements will daily trips outside, and perhaps some exercise around the yard.
They will be frightened their first few trips into the whole wide world. The feathers will come back in. Poultry feathers pull out easy when they are frightened.
So what is pied exactly? Mostly white? Or any color with white on it besides the head? Most colored muscovy have white at the shoulders don't they? They aren't pied?
It's not hardware cloth. It's a bit stiffer. I can find them around here at the farm stores. The spacing is I believe 1/2 by 1 inch. It stands roughly 3 feet tall and is 10 feet long. We zip tie it into a circle and it can stand alone. If necessary you can attach a top with bird netting or...
I personally would quickly scoop the ducklings up and put them in a 5 gallon bucket for transport. I use this method for all my young poultry I put out during the day. The bucket gets laid on it's side in the outside pen and works as cover, as well as heating up in the sun like a little brooder...