Number 1: If an item is downloaded from the store again and you have not removed the orginal item (as in when customer service initiates the download to replace one you reported an issue on) the old item is automatically placed in the trash and the new item shows the old play count. Although I have never done this with a song, only movies and TV shows.
Number 2: You are seeing two versions because there are two versions one in the cloud with 0 plays because you didn't play it and one on your device with X number of plays. (Bet you money you are seeing this on your iOS device)
Number 3: The option you are talking about just turns off the ability to see the cloud version. It doesn't delete it.
Number 4: As stated earlier, even if your hypothesis were correct: the play count would be zero (0) and not partial for movies and TV shows. Remember there is no partial play for songs.
Number 5: I don't have an iOS device! (I stated this very clearly) That is where you normally purchase items in the cloud. I am using a computer and downloading my purchase.