It is possible that Termina is an underground world within the earth where people go to hide.
Think about it, Link fell down a hole.
If Termina was *underneath* Hyrule, then how could it possibly have a sky, a day-and-night cyce and its own Moon? If it was *underneath* Hyrule it would be nothing more than a huge cave, which it clearly isn't.
-Fairies only exist because of the Deku Tree, yet he doesn't exist in Termina. So where do Tatl and Tael come from? What are the chances that they weren't paired with Kokiris, and then find the elusive portal to Termina as Skull Kid did?
Nowhere does it ever say that fairies exist because of the Great Deku Tree. They exist in every single Zelda game, the vast majority of which do not feature a Great Deku Tree.
-The reason why the people look so familiar to their counterparts in Hyrule is possible to do their relatives escaping underground and establishing their own nations. This also explains why there are no Hyrulian counterpart to Kafei, Pamela and her Father, Tingle, and the Mayor and his wife. An example of this would be Romani, who has a sister and no father. While in Hyrule, Malon has no sister nor mother, but has a father. Cremia never states she has no mother, even though she never appears; MM Talon is also not related to her or Romania, oddly enough. Interestingly, Cremia has a Triforce on her person. From this, we can gather that OOT Talon is Cremia and Romania's father, and Romania's unknown mother is Malon's mother.
OK, this makes no sense either. Let's take Anju as our example. You're saying Anju resembles the Cucco Lady in OOT because they had a shared ancestor who left Hyrule and went to Termina. Let's look at it logically. Anju's grandmother is present in Termina. She is the counterpart of the woman who runs the potion shop in Kakariko Village. So at the time Anju's grandmother exists in Termina, another woman who looks, sounds and acts exactly like her lives in Kakariko Village but has no connection to the Cucco Lady. The idea of relatives escaping to Termina seems very, very doubtful.
By this logic, the Terminian Talon who runs the Milk Bar would have to be the twin brother of OOT's Talon, since the only reason the counterparts look alike is because they are related somehow. Funny then that Cremia and Romani never mention their Uncle, especially when they do so much business with him. Funny also how OOT's Talon and Malon never mention this guy either. Again, this whole paragraph seems doubtful as their are too many questions raised and virtually none answered.
Koume and Kotake do not die in the child timeline, they die seven years in the future, in the adult timeline. To avoid persecution by the Hyrulian King, they could have escaped and changed their lifestyles.
Koume and Kotake are described as Ganondorf's surrogate mothers. What exactly that means is anyone's guess but the one thing we can agree upon is that they have an incredibly strong bond with Ganondorf. Considering they essentially desecrated the Gerudo's sacred temple in his service, the idea that they would just leave him when the King was trying to bring him to justice does not fit their character at all. The Witches would almost certainly have stayed to fight alongside him and probably would have been willing to die if it helped advance Ganondorf's position. In MM, the Witches are too different from their OOT counterparts for it to be likely that they are literally the exact same characters.
-Ever heard of the hollow earth theory? Some deviations state the likelihood of a second planet or universe within the earth itself. This explains how the eerie moon in Termina is not seen in Hyrule, or how the impact of it affect the sequence of events in Ocarina of Time (Adult timeline) or Twilight Princess; though one can argue that both take place in the event that Link succeeds in his quest rather than fails, which occurs in another timeline. Moreover, the changing of time in Termina does not seem to affect Hyrule, from what we know; in fact, the Song of Time does not have the same affect in both realms. On top of that, there is the existence of aliens in MM but not in OOT (further proofing that a separate universe exists within the earth).
The Hollow Earth Theory has been conclusively proven totally, 100% wrong. It was dismissed completely about three hundred years ago because it is known to be incorrect. It simply makes no sense and defies all rational logic.
As for the changing of time not affecting Hyrule, how do we know? All that happens is time is rewound 3 days and the events play out exactly the same way without Link's intervention. Hyrule could well be rewinding as well but since everything would happen the exact same way after each rewind, no one would notice and it wouldn't cause any issues.
As for the different effects of the Song of Time, this is just speculation but, perhaps the users *intent* changes how the Ocarina works. In OOT, Link only ever used it to open the Door of Time and move those blocks. But when he uses it in MM, he does so knowing that he must have "more time". He plays the tune and hey presto! He has more time! Just throwing that out there.
And how you figure aliens proves that there is a world *within* Hyrule, well, I'd love to hear exactly how you came to that conclusion.
-Also, there are no counterparts to the three goddesses, or the Triforce. There are also no counterparts to the Fierce Deity or Majora (although one can say 'Link' and 'Ganondorf', but if both were to be the counterparts, then surely the Triforce would exist, or at least a variation, which in turn would demand a counterpart to Zelda, which there is none).
I can't argue on this point but it is worth mentioning that Stone Tower does have images of the Triforce all over the place. There's a very interesting theory related to it called the Stone Tower of Babel theory. It's a fascinating read so I recommend you look it up.
-There has been much controversy whether the Interlopers in Twilight Princess are Terminians. It is possible that Termina is the place where Interlopers escaped to; or the supposed Twilight Realm, which explains how the Happy Mask Salesman acquired the mask in the first place.
So Termina *is* the Twilight Realm? And that explains how the Mask Salesman got Majora's Mask in the first place? I take it you're basing this off the Fused Shadows resembling Majora's Mask. Fair enough, but seriously, do you remember the Twilight Realm? Remember how dark it was, how forboding it was, how it seemed to be made of various floating rocks? Remember how the inhabitants were their own race of weird looking... Things? The Twilight Realm and Termina are nothing alike and to conclude that they could be the same place based off of almost nothing is a bit farfetched.
-Furthermore, the technology of Termina is more advanced of that of Hyrule in OOT or TP, even though TP is supposed to take place further in time than MM. Things like the clock tower, fireworks and pictograph come to mind. A bit far off for a 'parallel word', huh?
Just because the technology is somewhat more advanced doesn't mean Termina can't be a parallel world. The technology has nothing to do with it.
Personally, I think this sounds more ridiculous than the idea that Termina is just another country (and boy, *that* idea is very ridiculous). Your reasons for thinging this seem weak and ill thought out and don't seem to be based on reliable facts. I would say this theory is very unlikely.
Also, I want to just say sorry if my tone seems like I am mocking this theory or being overly aggresive in my disagreement with it, that isn't my intent at all. Just pointing out why I think this is unlikely.