I think we are expected to understand that The Doctor being able to prompt healing in River, is because she was given the regeneration ability from being conceived in the TARDIS while it was travelling through the time vortex. She isn't able herself, as she apparently used all her undisclosed regenerations to bring The Doctor back after she had killed him.
Typically a Timelord might use regeneration energy on themselves. Although that's a modern NuWho concept, that's not really utilised. Timelords, well at least The Doctor are portrayed as pretty durable, and death is the point that they use it, obviously.