It sort of confuses me.

Are you a mortal with the soul of a dragon? Or a dragon in mortal form?

Both basically.. You're a mortal born with the soul of a dragon, and in turn are basically a dragon in mortal form. Although I'm not sure how that works since dragon's don't really die.. but there are random dragonborn people in Sovngarde.

You are a mortal with the soul of a dragon. not a dragon. just a mortal who has been gifted the dragon blood.

Akatosh thought it'd be fun to stuff a dragon soul into mortal bodies....You can die because unlike dragons your body dies i.e is still mortal.

Actually, when that happens, I role play it out that when I die, Akatosh rewinds time as I load a save.
"Dammit son..."