What is the ruling on frowning or refraining from smiling at a female teacher who ridicules academic performance or appearance? Does this alienate her from religious people? And how can one respond to her in a gentle manner while being bold in upholding the truth?

Mocking people is religiously forbidden. It is prescribed for the one who is mocked to pardon and forgive, and to meet evil with good. If the mockery comes from a teacher by way of jest, patience is required, along with the possibility of engaging in a gentle dialogue with the teacher, and being soft in speaking the truth.