Immortal removes their maximum age limit. It does not stop penalties from future aging, nor does it involve a type change (generally to Outsider) that makes them immune to bunches of spells. They just get to be really, really old. I'd argue that it's somewhat worse than the druid 15 ability, quite a bit worse that the monk 20 ability, and not inappropriate at 13 at all.
Undying allows them to come back from dead once per day. It's a very narrow form of contingency that arguably drops all of their buffs when it gets triggered (because dead things are objects, not creatures, and aren't valid targets). That comparison does make me reconsider its level though, and I might bump it to 15. But it's really not that strong and doesn't preclude them just dying a second time.