Absolutely. In fact, if you ask to speak to a manager, and ask for the partial refund enough times, they'll even issue you a $40 Customer Service Gift Certificate along with a full refund of your Prime fee. The person you speak with may not be able to offer this on the first attempt, but if you stick with it, you'll get at least that much. Sometimes they'll even come wash your car in the deal.
No, not if you have used it. Copied and pasted from Terms and Conditions:
We will refund your full membership fee if you cancel your Prime membership before you or your invitees have made any eligible purchases and before you have taken advantage of any Prime benefits, such as Prime instant videos or the Kindle Owners' Lending Library. You are not entitled to any refund if you cancel after you or your invitees have made any eligible purchases or after you have taken advantage of any Prime benefits.