I would recommend putting a word option other than "हाँ" since that word could also be used in the same context. "हाँ, वह नहीं पीती है", or "Yes, she does not drink" is also a valid answer in context such as a question where the person asking the question is making the person responding feel inclined to say yes. I think instead of "हाँ", it should be something completely wrong in order for the person studying to emphasize on the नहीं part.
I agree. Whether you start the sentence with हाँ or नहीं totally depends on the question being answered. Without context you have no way of knowing which is correct. "Does she drink? No, she doesn't drink" vs "Is she a tea-totaler? Yes, she doesn't drink."
Can someone explain the है here? I thought when negating something in the present tense, you dropped the verb होना
No it wouldn't. Look carefully at the verb.
For a female we would use पीती, but for a male we would use पीता.
नहीं, वह नहीं पीती है - no, she doesn't not drink
नहीं, वह नहीं पीता है - no, he does not drink