When you get to Paradise, Mankar Camaron is wearing the Amulet of Kings How is this possible when it states that only Dragonborn can wear it?
It isn't exclusive to the dragonborn. The following is stated on the wiki
Only blood-relatives of Alessia can wear the amulet, otherwise it slips off the neck.
In The Book of the Dragonborn, it states that Reman Cyrodil was not related by blood to Alessia, and neither was Tiber Septim. The Book also suggests that there were others of the Dragon Blood not of the Royal line. So, that must make Mankar Camaron one of the latter. I believe the book The Dragon Break also corroborates that, as well.