I don't see any evidence that Link fell through a portal. Those masks appearing was solely an artistic decision.
When people develop games, they never include things that do not serve multiple purposes. Listen to any developer talk about the process of making a game for proof of this. The masks were an artistic decision, yes, but they also serve to show the moment Link falls through the portal into Termina.
Besides, it is an inarguable fact that Termina is a parallel dimension and is not connected to Hyrule physically. The only way for anyone to travel between the two is with a portal of some kind. That is what we see Link fall into at the start of Majora's Mask.
As for the "dopplegangers", they were used because Nintendo had to re-use the graphics from Ocarina of Time. The Zelda series is filled with dopplegangers that only change along with the graphics of the game.
Yes, Nintendo reused the same models so as to shorten the development time. That doesn't change the fact that all of them (except one) are completely different characters. Going back to everything having multiple purposes, reusing the character models cuts down development time and helps establish Termina as a parallel dimension to Hyrule. The mere fact that the same models are reused is a narrative device deliberately employed to let the player know Termina is a parallel to Hyrule.
As for the series being "filled" with doppelgangers, that simply isn't true. Yes, characters appear in multiple games (like Tingle), but this is always a different incarnation of that character, the same way it's different Link's and different Zelda's. Other characters, like the postman from Majora's Mask, postman from Twilight Princess and the postmaster Rito share a resemblence so as to create a 'theme' amongst their shared profession.
I think Koume and Kotake are the same witches from Ocarina of Time, but I won't discuss that here.
It's painfully obvious that they aren't. When Link first met the pair in Ocarina of Time as a child, they were fiercely loyal to Ganondorf and used their dark magic for evil purposes. They delighted and revelled in causing harm to others. In the timeline the leads to Majora's Mask, the two witches would still have been loyal to Ganondorf who was being persued by Hyrule's soldiers. Why would they leave his side to open a potion shop in Termina? Why would their entire nature change from borderline psychotic evil witches to pleasant, friendly old women who brew potions for general sale? Everything about their character is different in Majora's Mask and the only conclusion that can be derived from that is that it is not the same Koume and Kotake from Ocarina of Time but rather a parallel of the pair from Hyrule. Again, this helps establish that Hyrule and Termina are parallel dimensions.
Regarding Kaepora Gaebora and the Four Giants, I think Termina is pretty far from Hyrule, like, farther than where the giants walked. Besides, it doesn't matter, just because something is not mentioned (like Kaepora Gaebora going out of his way to say Hyrule was in danger) does not automatically mean said thing only exists in an alternate universe.
Firstly, again, it is established fact that Termina is a parallel dimension from Hyrule. It is not "far from Hyrule", the two places do not exist within the same dimension. That is fact.
I accept that just because a character does not mention a specific event, doesn't mean it didn't happen. But when the two locations for these events are seperated in the way Termina and Hyrule are, it hints that events in one world do not affect the other.
You also say that Termina is far enough away from Hyrule that the Giants could walk and not be present in Hyrule. That's pretty darn far. The distance between Hyrule and Termina, according to you, must be frightfully huge. How do you explain Link travelling that huge distance by falling through a tree? Link fell while still in Hyrule and yet turns up in the middle of Termina. For the two lands to exist together but be far enough apart for the Giant's to leave Termina without entering Hyrule, Link had to fall through a wormhole or portal. He could not have travelled thousands of miles to the west by falling straight down.
Sir Arthur Conan Doyle once wrote,
"
It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts."
Your theory completely ignores facts, cheifly, the fact that Termina and Hyrule are seperate dimensions. Once you ignore that, any and all conlcusions you draw are simply wrong as a direct result. I do apologise for being a huge downer on your theory but all the evidence that disproves it is right there and has been presented throughout this thread by multiple people.