Question 2. Could this sentence mean “I am becoming a duck?”
Question 3. If someone wearing a duck-like costume is asked “What are you pretending to be?” at a Halloween party, could he/she answer “I am being a duck?”
Regarding the third question, I do recognize the sentence could be grammatically correct, but limiting the scope of discussion to spoken English, how common, in terms of frequency of use in casual conversation, is that sentence?
When ‘be’ is used this way, it usually means ‘acting (like)’ or ‘behaving (like)’.
For example, if a mother hires a babysitter and phones just to check on how things are going while she’s out, the babysitter might say ‘Don’t worry. Everything is fine and the kids are being angels.’ – i.e. they are not misbehaving/they’re acting like angels.
No, I would not interpret your sentence to mean “I’m becoming a duck.”
I think this would be unlikely. People would be more likely to say either “I am a duck.” or “I’m supposed to be a duck.”