1) When is the last day to drop a course?

To do so without paying any fees or showing up on your transcript, it is usually 2.5 - 3 weeks after the semester begins. Although, you can still discontinue a class after this; it will show up as DISC on your transcript and you will unfortunately still need to pay. The deadline is usually in the third month of the semester (usually after most midterms), so you can estimate and judge your expected grade based on those results (please note: this is just an estimated date and does NOT guarantee your midterm will be before the date).
You can verify the current drop and disc. For dates CLICK HERE