The reaper lore on Supernatural has always been a little messy.

I'm going to assume Tessa's appearance to Dean is based on the real girl she saw at the hospital and then decided to hop in her body because before that she was a creepy ghost reaper, which is closer to the creepy zombie reaper we got in Faith. Also why isn't everyone immortal if the reapers can't do their job, like they were previously or if not immortal at least being looked after by reapers?

I'm a little upset that the show never even acknowledged that reapers are possessing people now. Also being able to kill death is a tad oxymoronic. It's not like supernatural to be this uncertain with their lore.