She's most likely a white layer.
@WannaBeHillBilly has white layers and I think a few of them have had injuries to their legs, maybe he can share what he has done.
They are pretty ducks you have there.
Yes, definitely a White Layer: Fleshy bill and blue eyes. And no, my White Layers have grown up with mostly Runner descendant breeds and are therefore well trained and never had leg problems, other than bumblefoot. (My Black Swedish Magpies do have frequent leg problems, but i assume this is genetic.)
Bazilla Duck had a mild heat-stroke after an exceptional hot day but recovered in a dew hours, so their very dense feathers is their weak point during the hot summer months. They need plenty of water bowls around to cool off.
In regards of the leg, there is not much you can do, other than swim time
without Epsom Salt in the water. Epsom salt helps with superficial wounds but has no effect on stretched ligaments, bruised muscles or twisted joints. But if she ingests some of her bathing water - and which duck wouldn't? - Epsom salt will cause diarrhea and loss of minerals. Swim-time and rest will help.
And once she can walk again, she needs exercise, running from here to there and back elsewhere to develop strong legs and muscles. Heavier breeds tend to stuff themselves and then lay down somewhere and rest. Keeping some distance between their food and their water is a first step.
- How old is she?
- Has she started to lay?
With the food problem: All my younger ducks weren't eating pellets, but they all ate crumbles with vigor. Try to grind some pellets up for her and see if she likes those. And opposite to what is commonly said: Some ducks have a very keen sense of taste! She may simply dislike the taste of the pellets. My Ducks love the cheap cat-food from Kroger and Dollar General. I once bought a really expensive bag of Purina, tried feeding it in the morning and most just spit it out and looked really disappointed at me.
Coming to the next point: Injured ducks need extra protein to heal! Try to feed her some dry cat food, then later mix some (crushed) pellets in between to get her taste buds adjusted.