2. money or financing is like any other commodity. It is bought and sold each day. You normally are going to see the interest rate change based on the number of points you are paying. If you are receiving a no cost no points alone, I assure you there is a higher interest rate involved. If you want to buy down your rate, you would pay additional points.
3. The lender wants to see your loan go under the percentage ratio required for PMI. I don't think you would normally be able to eliminate that insurance in a period as short as six months.