The only part of your theory that's even plausible is the part stating that MS can be awakened without killing your closest friend. That has already been proven in the manga with the info that both Madara and his brother awakened MS. Everything else is pure speculation not supported by facts.

EMS is obtained by stealing your brothers eyes. Both Itachi and Madara have confirmed that. Once Madara went blind there was nothing that he could do to regain his sight, so his brother offered up his eyes. That's also when a new and final secret of the MS is unlocked, and we have to assume that it's the immortality at this point. Nothing else about Madara's unique MS has been revealed.

After Sasuke and Madara talk, Madara asks Sasuke what he will do with Itachi's eyes, "will you transplant them?" And Sasuke said no. So no EMS/Immortality for Sasuke.

I don't think Shisui learned anything about Itachi's mission. I in fact believe that Itachi's mission was to kill Shisui to gain the MS. Itachi told the police force that he missed the "meeting" because he had a mission. And I believe that mission was to kill Shisui and gain the MS. Having it would make it that much easier for his other mission of annihilating the Uchiha clan. After he told them he had a mission, they told him that the only other person missing from the meeting was Shisui.

Madara and his brother were not competing for control of the clan, they were competing with each other and through that fierce competition, were able to unlock the MS. As a result they took control of the clan and Madara was made the leader.

I'm sure that Gai sensei has never opened his gates while fighting Kakashi. That's highly unlikely. Gai was never trying to KILL Kakashi, simply spar with him.

Sasuke unlocked his MS by witnessing the death of the person closest to him, Itachi with whom he shared a bond even stronger that the bond he shared with Naruto. This bond of hatred was so deep that Itachi was the closest person to him.