Eye exam: should I take off my eye makeup for an eye exam?

Not necessary. If you are having a general eye exam, you do not have to take off makeup. If the doctor feels that it is necessary, the staff will remove your makeup for you. Unless you are instructed otherwise, you do not need to change your cosmetic use.
Depends. Generally no, but if your complaint is about the lids of your eyes the physician would want to see that area and it could be obstructed by make-up. I would recommend you not wear eye make up or especially heavy eye make up for the exam. You should consider leaving off eye liner and mascara if possible. The doctor will thank you. Put it on after the exam.