The Time of the Doctor - S7-E17
Other mistake: While looking around the Doctor's room, one of the children's drawings Clara passes by has the TARDIS in it... when the TARDIS has been absent for all of the 300 years the Doctor has spent on Trenzalore up to this point, so none of the pictures existing now should have the time machine present. And it's not a particularly weathered picture, either, suggesting it can't be from the beginning of his stay on the planet. (00:31:47)
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.