Sure. But is that inconsistent with anything GP said? If you look at the list[1], I think you'll see that the sites are obviously not all cathedrals by that definition. The Wikipedia article doesn't claim otherwise; it calls them "sacred sites dedicated to the Archangel Michael." In fact, two of them are just islands named after St. Michael. Another is a religious site, but one that is not dedicated to St. Michael—rather it is located on Mt. Carmel which is associated with St. Michael.
Yes, but a bishop is not ever going to (and could not ever) reside at a monastery because it would be incompatible with their job as a bishop to do what monks do (retire to a life of prayer and contemplation). A bishop is the boss of all the diocesan priests, so needs to be a secular priest not a religious.
The word cathedral comes from a Latin word meaning “seat.” The seat referred to is the seat of the bishop, who is the leader of a group of churches related to the cathedral. The bishop's seat is both a metaphor for the cathedral as the bishop's “seat of power” and his actual chair, the "cathedra," inside the cathedral.
Strictly, it's a Greek word meaning "seat" (καθέδρα), although it was borrowed into Latin with what I believe is a more restricted meaning. There is also a Latin word meaning "seat" (sedes) which is also used to refer to the seat of a bishop (an episcopal see)!
[1] https://en.wikipedia.org/wiki/Saint_Michael%27s_line