Can somebody explain: originally, the regeneration limit was 13 right? Did this change when the universe was reset?
It's been explained in previous stories (going back to Trial of a Timelord or one of the other Gallifrayen episodes around then), that the ruling council can gift additional regeneration cycles for exceptional service.
From memory in one of the stories the Master was given an extra regeneration, and in another he was aiming for a full regeneration cycle.
There have also been stories i think, where the master was trying to steal another timelord's remaining regenerations (I think a bunch of master stories have basically been about him trying to get more lives because he's wasted them in failed attempts to gain power).
IIRC basically between the TV series and the books, it's sort of implied that the 13 regenerations is a cultural and technical measure, imposed to help limit the population.
In one of the books for example the Doctor goes to his original "house" where you find out the timelords are basically created from a semi random mix of DNA by technology that is part of the house, to sustain it's numbers - I think the story was partly about how there was a potential uncounted/documented "birth".
They'll fudge a retcon around the regeneration limit when the need arises.
Didn't the weapon represented by Rose Tylor's image basically say "your punishment is that you'll live", suggesting that the weapon has some way of accessing the same powers the council could use - it also ties into the way that Rose when she had the power of the heart of the Tardis was able to bring Captain Jack back to life (although in a rather less controlled manner).
I think I've said it before but the impression I've got a few times since the restart of the series and the time war, is that given the link all the Tardis units have to Timelord's power system, it could be that the Tardis itself has some ability to help with regenerations (also ties in with Pond's daughter getting some regenerative abilities due to conception in the tardis), possibly something the council did to make their fighting personal more effective (ties into the "additional regenerations for exception services" neatly - if you're sending out warriors in Tardis units knowing they're likely to get badly hurt, the ability to regenerate would be handy).