1) Warranty periods start upon original purchase, because warranty service costs are part of the selling price of the device. When you got a replacement, you did not pay for it, and thus no warranty extension. All companies work this way, and understandably so.
2) Warranty claims are dated by the time you report the issue. If you waited 3 months to report, then the onus is on you. However, if you report an issue before warranty expires, and the condition exists after it expires, the company is still obligated to service it because you first reported the issue before expiration.
3) If you got 2 lemons, time to move on to another model.