Although your reasons are just questions and not definitive evidence, you are right that Termina being in Link's head is not true. There are numerous reasons to say this.
First and foremost, Hyrule Historia, the Majora's Mask manual and various developer interviews tell us very clearly that Termina is a parallel universe. They never even hint that it is a dream, nightmare or some other kind of sub-conscious realm. Neither do they even suggest that Termina is a forgein land, physically connected to Hyrule, but that's an entirely different but equally incorrect theory some people have.
Despite actually being told outright what Termina is, some people still argue that it was all in Link's head. Some people say that the trials Link faced in Ocarina of Time scarred him mentally and left him with a mind that was either "warped" (as VanitasXII put it) or in need of repair. If that was the case then, well, surely every adventure would scar Link mentally. If that was the case then every single Link who ever went on an adventure would be reduced to a loony by the events they lived through but we know that's not the case.
After The Wind Waker, we know that particular Link went on to be perfectly sane and experience Phantom Hourglass. After Legend of Zelda, we know that Link was sane and went on to experience Adventure of Link. A Link To The Past's Link didn't seem to have mental issues in Link's Awakening and there was never any reason to think Link had some kind of post-traumatic stress after Skyward Sword, Minish Cap, Twilight Princess or Spirit Tracks. Why then would the Hero of Time succumb to some kind of psychosis?
The claim he was mentally disturbed holds less weight when you consider what we know of Link's actions before Majora's Mask. In this particular timeline, Link has experienced all of Ocarina of Time, fought and defeated Ganon and been returned to childhood by Princess Zelda. At the end of Ocarina of Time we see Link, now a child again, approach a young Zelda. Cue curtain and the standing ovation. Hyrule Historia gives us more details on what Link was doing there.
Link went to go see Zelda to let her know that the dark premonitions she had been having were true and to warn her that something had to be done immediately. Link spent a few days at the castle, after which Zelda gave him the Ocarina of Time. Hyrule Historia tells us Link borrowed Epona from Lon Lon Ranch after a couple of months and then rode off to go find Navi.
Considering what Link has seen and experienced, these actions are incredibly sane, deliberate and sensible. He obviously understands the concept of time travel enough to seek out Zelda on his own initiative since no one old him he had to warn her of Ganondorf. Remember, Zelda sent him back in time as a reward, she was trying to give him his childhood back. It was Link who realised Ganondorf was still a threat and he took action to stop him. Getting Epona showed planning and preparation for his journey to find Navi. He didn't know where she was and instead of just running off blindly he took plenty of time to make sure he was ready for what could have been an incredibly long journey. If he was haunted by the horrors he had witnessed to the extent that he ended up imaging an entire world with arguably worse horrors it's very doubtful he was in any state to make such rational, well-thought out decisions. His entire mental focus would have been himself, instead of Hyrule as a whole and then Navi.
People who support the whole "in Link's mind" theory generally use the reappearance of familiar faces as evidence but that very logic makes characters like the beavers, Kafei, Kamaro, Mayour Dotour and his wife, the Indigo-Gos, Pamela and her father as well as Igos du Ikana and the Deku Royal Family make little sense. Where did Link imagine them from if most everyone else is just him remembering faces?
Either he imagined the entire world from scratch or the whole thing was based off of memories already there in his mind; a mixture of the two seems very unlikely.
Sorry for rambling on but I just find the idea that Termina was all in Link's head (and the idea that it was a forgeign land) something I have to speak against.
