I would not use lard it will cause wet feather. Her feathers don't look bad at all dry so she must be doing some preening you just haven't seen it. I dont always see mine, preening either. As for her feet can you post pictures? and make a video of her squeaks one of my Muscovy sounds like a bird instead of the usual Muscovy noise they make so it may not be anything to worry about, Bringing her inside where it's warm then taking her outside where it's cold could cause problems though. Since she is white seeing mites on her should be easy since mites are blk and move check under her wings making sure to get to the skin also mites like to hang around the vent area too. I use Ivermectin pour on on my chickens to keep mites away I put it on the back of their necks just like you do the flea repellent for dogs. I haven't ever had mites on my ducks since they have water to bathe in it helps keep the mites away But if your chickens have mites and you can't offer bathing water for your ducks since it's winter, then she could have them. What are you treating your chickens with?