poor chicky!! you've got to secure your coop the best you can if you free range them you may want to keep them up for a few days but I'm sorry to say it will be back once they find a free meal they just keep coming back it sucks im sorry!
We have khaki Campbell's assuming most ducks are alike ..ours lay all year round, but then again we live in northwest fl so it doesn't get extremely cold and snowy here.
They should be fine . Ducks and chickens cannot transfer diseases to one another. They may bicker a little because they're just getting used to each other. Be very careful having a chicken hen in with a duck drake though if the drake tries to mate the chicken hen he will seriously hurt her...
Can you see any obstructions in its throat? may be as simple as gettin an eye dropper or syringe and flushing some water down its throat or you may need to check for gape worm which as far as I understand you can see if you look down its throat. Ive never had experience with gape worm before so...