Maybe cause Tobi found him before he met Jiraiya?
They were definitely younger than 12, man. Age and looks in Naruto tend to be a bit unbalanced, idkw. And where do you get 11 years from? What are you accounting for?
So far as I've looked into it, all we saw when his parents died was him to start to cry, get angry, and then it cuts to him waking up with the Rinnegan and the two shinobi. Tobi probably made him blackout and killed those shinobi, then while he was out cold, transplanted Madara's Rinnegan into him. If he really did have it transplanted, that would've had to have been how it happened. As for the Byakugan, it's most likely related to the Sharingan, but Kishi would have to explain their connection further first. It can't be one of the three great dojutsu and not be heard from since part 1.
Yeah, he couldn't have been more than eight or nine in that flashback chapter. He probably met Konan and Yahiko a few days after their deaths and Jiraiya maybe a month later, so had they started training when he was around nine, he definitely could've learned 'em all by ten.
BTW, wasn't this thread supposed to be about the best prodigies, not the old "Tobi gave Nagato the RG" theory?