I thought it was his grandmom or something that gave him his nickname, after which his little sister kept using it all the time that and so it spreed to his friends so he had Kyon as nickname even before Haruhi started calling him that.
Also this took me way to long to realize but with Kyon going back in time and helping Haruhi paint the grounds it gives Haruhis (Before she cut her hair) question to Kyon if they've met before a different meaning.
I'd rather not think of Asahina as Kyons sister, for one there's the whole incest thing and the fact that Asahina (adult) seem to miss Kyon which implies he doesn't exist in her time not to mention her whole line to Kyon telling him not to fall in love with her since it's more or less implied that she harbors feelings for him as well. So if they're siblings she wouldn't miss him unless he's dead and if that's the case she probably wouldn't let him die. Also she wouldn't really be so awkward around her own brother considering the difference in how his sister treats him and Asahina unless she's one heck of an actress.
My interpretation was that shy Nagato doesn't have any powers at all and that the needle probably changed shy Nagato back to alien Nagato and thus she was able to change the world back. While Haruhis powers may lie inside shy Nagato in some form of dormant state I still think of her as a normal powerless girl.
I wondered more about Kyon than Nagato. Ok so we know he spent 3 days in the altered world and in the normal world during those 3 days he fell down the stairs and went into a coma. So which Kyon ended up in a coma? From what we've seen it's the altered version of Kyon that wakes up which should mean it's that Kyon but if it is what happened to the normal Kyon and where did he go? Who spent that day in school and ended up in a coma since altered Kyon doesn't remember that at all.
From the sound of Nagatos explanation all she did was use Haruhis data generating ability to rewrite the past. So in a way you could say that Haruhi created a big rock and that Nagato refined the rock into various tools. This works since Haruhi is merely creating a bunch of data without any knowledge and therefor leaves all the data scattered around and as long as she does that it means someone else is able to manipulate that data. So theoretically Haruhi should be able to change the past as well.
The question is were the data generating ability went after the Nagato rewrote the world since if the ability doesn't exist in that world how did they change the world back. Or is there enough data scattered around to be able to change the world back? Or does it lie dormant inside shy Nagato.