I frequently tell flock owners to feed all flock. It is nutritionally better than most layer feeds, but my birds still get layer feed quite often because there is quite a cost difference when feeding 70 birds. Personally I don't mix. If I have both I feed each one in different feeders.
The longer you get from hatch day the more likely Mom is to reject it. The injury might have happened when it didn't keep up or it might have been mom, but It is time for a new plan because now she does not consider it part of the brood. Taking another chick in to brood with it is a good plan...
What are your future duck goals? It would be much easier to find a new home for the duck hen then a home for 2 drakes. It is possible to keep only drakes.
If you want to keep the hen
Some will say you need to have more hens than drakes, but personally I keep ducks with only one hen per drake...
This is not angel wing, but it is a sign she is struggling. What are you feeding as their main food? Make sure she gets niacin DAILY. (The B complex or nutritional yeast)
Ducks hatch well using the same humidity as chickens. The humidity in the room will affect how much water you need if any. Aim for between 30 and 50 percent the first 25 days then up the humidity to 60-65 and go into lockdown.
If you only have one drake the drake doesn't need to compete for his hen(s). 1 drake with 2 hens should work fine. As they come into breeding he may be a bit rambunctious as he will be trying to get both hens to choose him.
Kalmbach makes an all flock feed. They call it Flock Maker. It comes in crumbles or pellets. 20%protein. I have not checked into the game bird food you mentioned (game food normally has an even higher protein %)
The crumbles are great for feeding chicks and birds of all ages. Add a calcium...
My simple answer to when can chicks go in the coop is as soon as possible. Integrating chicks is easier when they are younger. I have provided a heat source and a safe place with a chick size hole with newly hatched chicks. I have placed chicks anywhere between 2-6 weeks directly in the coop...
My hens hatch chicks in a coop with a ramp. What you should do may depend on your space.
I keep food and water in the coop when I have chicks. My Moms keep the chicks in the coop the first couple weeks. The first time Mom brings out the chicks we watch to make sure all chicks get back up...
My thoughts not backed by research Normally when ducklings are still following Mom the mom is not laying eggs. Since Mom is laying it gives a behavior to mimic that most ducklings don't experience.