probably becaue it was enchanted, only whatever the corination is allows whever to wear it, probably.
because he wants his line on the throne? that part would be rather obvious
you still do not have the right to the throne, even if im wrong. the septim empire is long dead, even if we had the rights to the throne (which dovakiin does not) we could not
The only thing I agree with you about is that being Dragonborn doesn't outright guarantee you the Emperor's crown - but I'd say that it probably lends you a considerable weight.
What everyone needs to remember is that there are two types of Dragonborn. There is the true Dragonborn, one who has the soul of a dragon. This would be people like Reman Cyrodiil, Tiber Septim, and the player character of Skyrim. Also might include St. Alessia, Uriel VII, and Martin. They can absorb dragon souls and learn shouts easily. The other type is dragonborn by blood, aka on who has the blood of the dragons. This is more figurative. It is a mark of legitimate authority and a sign of Akatosh's favor to rule. They do not, however, have the soul of a dragon. None of this seems to be passed by blood otherwise none of the Septim emperors after Pelagius I would have had the dragonblood and been able to light the Dragonfires.
The Amulet of Kings and the Dragonfires only needed someone of dragonblood, aka endorsed by the Divines. All true Emperors are of the dragonblood but very few are actually Dragonborn.
Mankar could have been either of the two.
The player Dragonborn is both. Paarthurnax comments on your dragon blood when you first meet him.