For the first part, why he doesn't have a formal education: Nog is living on a space station with his uncle and father. Not in a Ferengi society. The Uncle doesn't want to shell out for an education for the kid cause he's Ferengi and doesn't want to pay for things, and the father just goes along because he's kind of a doormat. There's not enough opportunity for job-shadowing that allows Nog to learn from a Ferengi mentor that's capable of teaching such things as literacy, so he remains ignorant. Also explains why he gets into so much trouble (aside from the bad influence of his uncle), as he has too much free time from lack of mentorship.

He also shows that he's very hard working when he applies himself. So, in addition to tutoring from Jake and probably Keiko, he just buckles down and does the work. Especially when he gets to the academy. He specifies in "Homefront" (Or "Paradise Lost", I don't remember exactly) that he's doing all right at the Academy. Not excelling, so he's struggling. Probably not the least of which is because he's behind in education as compared to his classmates.

Harry Kim got addicted to clarinet

Nog went up the ranks more quickly because of the war, which provided him with many opportunities. Also, his connections, which allowed him to intern on DS9 and the Defiant, again in the context of war.

Harry was on a ship isolated from Starfleet. If Janeway had promoted everyone who had the merit, she'd have had a ship full of commanders and a handful of captains by the time they got home. But most of those people would have had to keep doing the same jobs, anyway.

But the true reason for the discrepancy noted by OP is just down to the fact that Voyager's writing team just wasn't as good as DS9's (or they were held back from above). The only characters to have a meaningful arc on Voyager were the Doctor, and Seven. The others mostly just had to reset at the end of every episode to preserve the show's episodic nature.

Harry never got promoted because the writers never figured out how to evolve his function on the show. Now, I assign a small part of the blame to Garrett Wang himself: he rarely gave performances that stood out and made the writers want to write about him more. But most of the blame goes to the writers and show-runners.

For example, if they'd exploited dual crews more throughout the series, with more conflict, etc., Harry might have found a place. Imagine if the Maquis crew had had their own ship for a big part of the series? Harry, eventually frustrated at being passed over for promotion, might have joined them!

Hard work, dedication, and Lobes.

Janeway kept Kim on a permanent coffee-finding mission.

Maybe Janeway was just secretly really racist against Asian people. Just because society has left bigotry behind doesn't mean all members of that society have.

You can’t delete the duplicate?

My favorite part of the Harry Kim joke is that at the end of Voyager, he was a captain, but Janeway rewrote that timeline to save Seven of Nine, so she ended up doing a retcon on Harry's promotions from Ensign. Never my captain, that's for sure.

I feel like it'd be canon for him to be Naomi Wildman's first officer.

It might be possible Ferengi also have higher-than-human-average neuroplasticity and simply adapt easier - this might even aid in the on the job theory.

I think you're on to something.

Various Ferengi having a kind of genius foreign to Federation values is a recurring theme in DS9.

Nog, in particular, gets up to some antics that probably require some brilliance. I recall him hacking or circumventing things even early in the series.

In TNG Wesley has a hard time getting into the academy and one of the other applicants is a genius in his own right.

I feel like there was some affirmative action going on.

I see two explanations. One, perhaps by "reading", they're referring to reading of a lengua franca like Federation standard - Nog has learned and is capable of reading the Ferengi language, but not another. When dealing with other languages, the general expectation is either a universal translator is used or they pick it up as they go.

I feel like this is a potential argument alongside the increased neuroplastisity. Jake and Keiko would not have been able to help him learn to read Ferengi as I very much doubt they could read it themselves.

Still Starfleet seems to have educational requirements. In LD:"Something Borrowed, Something Green", Tendi mentions how she wouldn't have gotten into the Academy without having gone to high school, suggesting Nog needs the equivalent of a high school education to train to be a Starfleet officer.

Clearly The Sisko was better at persuading Starfleet / The UFP itself how politically advantageous it would be to have an officer from a world thar, not that long ago, had been expected to be the next major enemy.

Thinking on this, Nog's family had connnections to the Nagus (I'm not sure if it's revealed before or after his joining - but even if it's after the Federation has spies ) so his rise though the ranks could be as much about politics as it is about his raw talent

He wasn't stranded in the delta quadrant and also had a better boss.

I assmued it was Federation Standard (english) they were teaching him. It would make sense the Ferengi never learn since their prejudice towards the Federation

The Dominion War probably helped create some job opportunities. During the war, Starfleet was launching ships as quickly as they could. In addition, they have to promote to fill in gaps left injured or killed personnel. After the war, some people may leave Starfleet, others, like O’Brien, may take a reassignment that had been deferred, creating more opportunities to advance.

Promoted officers aren't always the smartest guy in the room. You have to be likable as well.