I think 507 was a bit spur of the moment, but I think it means he can live forever if he regenerates. He can die, as was put forward in EoT, but I think regeneration is limitless. And there are three reasons why the Beeb won't kill the Good Doctor off after 13:
1) Have you seen the fanbase?!
2) And the more boring, real-world reason, Doctor Who pulls in massive ratings for the BBC - they won't throw away that money simple because of a throwaway line said over 20 years ago. (13 was established in Mawdryn Undead, right? That was on Doctor Five. FIVE. That gave them another Eight Doctors to wrap the show up in.) Of course, now it's back and we're running out of bodies, BBC need to think of something.
3) THE DOCTOR PWNS.
As for the Ace thing, I just thought I misheard Dorothea, but I'd forgotten that Ace's real name was Dorothy.
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