Retranslation of some of the lines by Fate of Destiny from NF :
The name of the eye of Pein (Nagoto) as a child that changed is called Samsarangan (It wasn't Rasengan~~~~) [Apparently, the guy or the people at 2chan thought it was going to be called that]
Translation for the first part of the sentence before the comma is fine, but the second part says:
It was the eye that Rokudou Sennin, said to be the ancestor of shinobis, had.
It seems that Rokudou Sennin created all the current ninjutus.
長門は輪廻眼を発現して岩隠れの中忍を殺してしまったことを恐れている（我を忘れて人を殺した ため）Translation for this is okay, but the parenthesis says along the lines of:
(For the reason of forgetting himself and killing a person) [That's the reason why Nagato was scared]
"Thanks to you, Yahiko's life was saved." And Jiraiya praises him.
The three have grown to the level of defeating Jiraiya's kagebunshin.
Jiraiya, feeling their growth, tells them to live on their own and Jiraiya leaves the Hidden Village of Rain.