I think the reason that OoT is a Nexus point is that this is where the Door of Time is opened (literally) and the timeline can be broken for the first time in the games.
Now to address the Link is dead, Song of Storms, how did it happen etc. bit: There are two options.
Option #1, Link isn't dead. Termina is a parallel world to Hyrule and the existence of stuff there is (almost) completely unrelated to the existence of stuff in Hyrule (think Mirror Universe on Star Trek, there was an episode where a hologram from the "prime" universe was a flesh and blood freedom fighter in the mirror universe on DS9 it was screwey and I didn't get it). Essentially, stuff exists independently in the two universes but is similar and just needs a separate back story (like what was created by a closed time loop in OoT can be composed by two brothers in MM). No big deal.
Option #2 (I tend to go more with this one), Link IS dead and nothing that happens in Termina matters. Well, it matters to Link but not to anyone else. MM is basically Link's soul dealing with the fact that he died and nothing that happens in MM has any bearing on what happens in Hyrule. Link incorporates things from his life (people, songs, etc) into his near death fantasy and creates a new adventure to play out one last time before he moves on.
This raises two questions. 1. In the Link is Dead game theory video, they say Termina is kind of a Purgatory of a sort. It could be but it could also be a fantasy as Link is slipping away. There is a theory about the movie Grease that kind of follows the same logic. Sandy drowned at the beginning, the last person she saw was Danny so she incorporated him into her near death fantasy and that fantasy got more ridiculous (angels singing about cosmetology school) as her brain lost oxygen. 2. Even if it's a fantasy, that doesn't mean that al of the other characters are made up. Link was chasing the Skull Kid/Majora before he arrived in Termina and the Mask Salesman seems a little too helpful to simply be a figment of a dying boys imagination. I'm wondering if those two aren't there to help Link move on. I think the Mask Salesman is Death, the Grim Reaper, the Pale Rider etc. He is there to help Link along and either Majora is not as powerful as he is made out to be (the Mask Salesman helped feed the fantasy to give Link one last adventure to conquer) or the Majora/Mask Salesman battle is actually a battle for Links soul. If Link wins, then the Mask Salesman takes him to the land of milkshakes and unicorns, if Majora wins, Link goes to eternal torment. I mean, if you don't reset the clock in time and the moon crashes down, the mask salesman comments on your fate, that's odd considering you're already dead.
Either way, In this theory, the whole game takes place in a sandbox either of Links making (his own near death fantasy), the mask salesman's or Majoras or a combination of the 3. In that case, nothing that happens here has any effect on the rest of the Zeldaverse so there is no need to explain how this Link went back in time to teach Guru Guru the Song of Storms.
Off topic but you did bring up an interesting point about timeline splits Sir. In Skyward Sword, you fight The Imprisoned three times. Either just before or just after the second fight (don't remember), you learn that the beast is actually Demise. You then go back in time to just after Demise was sealed and became The Imprisoned and engage in a duel during which you skillfully stab him in the chest and absorb his essence into the Master Sword ending his terror forever and incurring his curse. Was there another timeline split here? One where Ghirahim did not go back in time? If not, what were you really fighting during those first three battles with The Imprisoned? This confuses me almost as much as the fact that Skyloft floats peacefully above an impenetrable cloud barrier and below the sun but it's somehow almost always sunny on the surface (below the cloud barrier).