As it stands, he's very much mortal. He could end up doing something that makes him immortal in a DLC, like BeerBarron pointed out, but currently he is a regular person who just happens to be better at dragon-related tasks.
No, we don't. People who aren't dragonborn have established Empires, and not all Dragonborn were emperors.
Good response Nerevar...good response
Brown-noser! I don't respect the above answer because its the typical pro-Bethesda answer.
If the PC of the next game was the child of an emperor, he/she/it would not become emperor.
Heck! If the PC was the emperor, he/she/it wouldn't become emperor.
Why? Because it doesn't jibe with the scrolls...varying six, race, blah blah blah!
A hero can shoot fireballs from fingertips but can't become lord over a cluster of hovels.
But to the topic, the only hero that was explicitly declared immortal was the Nerevarine. Side effects of the Corprus half cure. Took away the madness and deformities but left behind immunity to ageing, disease and emhanced strength and stamina.