Not necessary, because the argument advocates thinking about counting sheep. Even if someone cannot imagine a wide variety of things, as long as they can imagine sheep, the argument can still work.

Not necessary, because even if someone doesn’t normally have a difficult time falling asleep, they can still use the sheep-counting method when they do have trouble falling asleep.

Necessary, because if it were not true — if thoughts of sheep WOULD keep the person awake at that time — the a person would NOT be able to fall asleep by closing their eyes and counting sheep.

Not necessary, because the argument concerns a situation in which someone is prevented from sleeping by other thoughts. The author believes counting sheep is a solution in that circumstance. That doesn’t imply the author believes counting sheep induces sleep every time, even in cases when someone wasn’t being prevented from sleeping by other thoughts.

Not necessary, because the content of someone’s dreams has no relationship to the reasoning. The argument concerns how to handle thoughts preventing someone from sleeping. Once someone is already asleep, the author’s argument no longer applies.