1. A golfer swings at the golf ball and misses the ball completely. Does that stroke count?
2. A golfer stops their swing in the middle of the downswing. Does that stroke count?
3. Your club head comes off on the back swing and you complete your swing at the golf ball. Does that stroke count?
This situation was covered in decision 14/2. When a golfer completes a forward swing with just a shaft, no stroke is made because the shaft by itself is not a golf club. So no, the stroke does not count(but why in the world would you finish your swing without a club head? You will know the instant the club head comes off of a club and it is every easy to stop the swing at this point).
4. Your club head comes off on the downswing and you complete your swing and miss the ball. Does that stroke count?
5. Your club head comes off on the downswing and you stop your swing. Does this stroke count?
No it does not. You are considered to have checked your downswing voluntarily so the stroke does not count.
Your clubhead comes off on downswing and you stop your swing but the momentum of the club head causes it to fly into your golf ball and move it. Does this stroke count?
This situation is covered by decision 14/4. The stroke itself does not count, as you voluntarily stopped your swing. However, you will incur a 1 stroke penalty for your equipment causing the golf ball to move. You must also replace the golf ball to its original position.