Would the prayer of one from whom a wind was actually emitted, but who thought it to be a mere misgiving and prayed, be accepted? And would Allah accept deeds similar to that?

The prescribed approach for the one afflicted with obsessive doubts (waswas) is to disregard and ignore them, because their worship is valid in this state. They should not pay attention to Satan's deception. They must not rule that wind has exited unless they attain absolute certainty about it, such that they could swear an oath to it. Otherwise, they should act upon the original presumption, which is that nothing has exited.