It's been a long time since I've seen "The Apple", but my memory was that it was simply said the elder Mallory helped Kirk get into the Academy without specifying what he did to help Kirk. It may have been a case of tutoring him to prepare for the entrance exam, or securing him one of those testing spots Wesley got in "Coming of Age".
The Bajorans and Ferengi have explicitly said to not
be Fed worlds, for those questioning the matter. In the case of Ro, Sito, and the various other Bajorans said to be in Starfleet, they likely escaped Bajor or came from a refugee settlement and made contact with some Starfleet officer at some point.
Nog joining Starfleet was a terrific idea. It permitted him to be part of almost all war-related stories, and ironically, it seemed like he had more to do than Jake most of the time. From what I've heard Aron Eisenberg didn't think it was such a great idea at first, but just as with Rene Auberjonois and the notion of Odo finding his people, he came to see it was a great development. Honestly, it's hard now for me to imagine a time when Nog wasn't an officer.