You are a nursing student, yes? You understand more than many of us about some things. Yes, ducks can be given penicillin. I am not an expert about types of antibiotics and dosages. But there are some archived threads where people share what they have done.
I don't know. If you do, you may have some bleeding to deal with. I wish I had more detailed information for you.
There is an Emergencies Forum. But duck questions often don't get responses - pretty much most who know about ducks just spend their time on the Duck Forum. Thinking out loud...
Another source for help may be a waterfowl rehabilitator - they might have resources and information for the specific injury. You can get oral antibiotics at a feed store, should you decide to try that route. I would not be hasty to euthanize the duckling at this point - I would explore...
Make an Epsom salt solution with a tablespoon of E.s. and a cup of lukewarm water. Don't let the duckling drink any of it, it is a laxative.
Either gently hold the duckling so its foot is in the E.s. water, or soak a clean cloth and wrap that gently around the foot. Hold it there for five...