The idea for teleportation was that he could warp to any unoccupied space within 50 feet of himself.

As for immortality, he's died before (5000 years ago) and come back as a mummy. The "resurrection" bit was more that if he's killed by conventional means- dismemberment, injury, gunshots, weapons, etc.- that he'd come back at sunset. He can still be permanently killed by destroying his body or sarcophagus (both closely guarded secrets) and can only resurrect once a week.