Re: How do some sharingan have special non mangekyou abilities?
I can come up with a few random short theories, some more believable (i.e fewer assumptions than the others). Kakashi's MS may be a weird Sharingan too it seems.
1.) Simple genetic mutation given Kishi knows a little about DNA and incorporates it into the story. Just like anyone, before say Shisui was born, he had a unique DNA sequence for his Sharingan that gave him this ability, such that his Sharingan was eye was unique from the day he was born.
2.) I was thinking of this. We know that you must fulfill certain emotionally straining requirements to awaken and evolve the Sharingan in the number of tomoes and to the MS. What if Shisui underwent an event that only partially shifted his Sharingan from the standard 3-tomoe, but that it never made it to the MS. Again this could be due to mutation, or something else.
3.) Another possibility is if it's not just about the Sharingan eye itself. What if it's about a combination of a Sharingan doujutsu with a user invented ninjutsu (Danzou had both Shisui's arm and eye. While the arm housed 10 Sharingan for Izanagi and Shisui's arm may have been most convenient, it may have been involved in the mind control jutsu). While the Ameratsu for example, is a pure doujutsu, if one combined a ninjutsu with a doujutsu, maybe they could create a new technique that's neither a pure ninjutsu nor a pure doujutsu.
There's some other stuff I've thought of, such as breeding with clans from the younger son's lineage, but these are just three off the top of my head.