Not if it's been going for about 10 seconds, but for it to be just sounding as you touch down would imply that the aircraft is flying about 5 knots faster than the slowest speed at which it can fly in that configuration, which is just about perfect for landing.
Quite correct, assuming a good calibration of the stall warner. I would expect the stall warner to do its thing in the hold-off. You might want to try some slow flying in your approach configuration to check this. Some can be a few knots out. As ever, talk to your instructor