correct words

The beak, bill or rostrum is an external anatomical structure of birds which, in addition to eating, is used for grooming, manipulating objects, killing prey, probing for food, courtship, and feeding their young.

So, either "beak" or "bill" would be appropriate for the first part of your question.

As for the second part, "off" and "from" are both "correct", so, again, the choice is yours.

Thank you very much, Contrex.

For some reason I find it most comfortable to use bill in association with ducks (and the playpus) and beak in association with birds that have a pointed oral appendage.

bill is the hard pointed or curved outer part of a bird's mouth (Oxford Advanced Learner's Dictionary)

It is not specified that 'bill' is reserved for certain birds?