them witnessing Rins death through their shared eyes is what activated MS for both of them. i dont think Kakashi killed Rin (at least on purpose) but that is what had to have activated both MS's. My theory like many others is that this is all a genjutsu set up by Madara where he somehow has captured the real Rin and he did it manipulating the mist and possibly even Kakashi. Or, Kakashi simply was a zetzu clone. Either way, Kakashi wouldnt feel guilty about not protecting Rin if he had done it on purpose. Unless she pulled a Yahiko, Kakashi wasnt with Rin when she was killed.
Itachi didnt kill Shisui, he killed himself after giving Itachi one eye and i guess Danzou the other, or Danzou somehow got it. Itachi gained the MS i believe by killing his clan (probably his parents). He did kill the clan in order to protect Sasuke and the village.
Sasuke witnessed Itachi's death, and he believed he had actually killed Itachi when in fact Itachi was dying anyways and kinda just...died. The link seems to be witnessing the death of someone close. Sasuke was close to his parents, but probably closer to Itachi if that makes sense and Itachi closer to the parents (him and his dad were pretty tight)
Same stuff with Madara and Izuna....so on....if im wrong correct me but this is what ive gathered/know/think