As per this statement, "If there's minyan of ten people and one person is praying a lengthy silent Shemona Esheh, it's preferable to wait for him, however, if there are needs such as if the minyan will separate or if it's a bother to congregation to wait, they may begin Chazarat HaShatz even though one is still saying Shemona Esreh" a minyan still seems to be a cohesive and singular unit even if everyone is not saying the same thing.
In my siddur, the Vidui said each morning has a section which, it says, is only said with a minyan, and a section which one could sing as an individual.
If I am davening with a minyan, but that minyan does not have the tradition of saying vidui every day, am I davening in a minyan (so I can say it) or as a yachid, since the rest of the minyan didn't say it (so I can't)?
And if I am in a minyan that DOES say it, but I have fallen behind because I daven Shmoneh Esreh slower, when I get around to it and the minyan is already elsewhere, am I still "part of a minyan that says it" or am I not part of the minyan so I should not say it?