Link dies in the Regular Ending but survives in the Good Ending.
Seagulls rarely rarely venture far out in the sea, and Marin turns/gets reincarnated into one in the "Good" ending.
Marin was always a seagull.
Marin was simply a seagull that was caught in the same dream as Link. The Nightmares are the only actual inhabitants of Koholint, hence why they're the only ones aware of the world's true nature. The NPCs are all merely people and animals that have been trapped in the same dream.
In that same vein, Tarin may have really been a raccoon (tanuki?) who simply remembered his true form when he ate that mushroom instead of being Baleful Polymorphed into one.
The Wind Fish is incredibly ancient, and has seen other Nintendo universes.
It'd explain not only why Koholint is a mishmash of elements from previous Zelda games, but also the presence of Goombas, Piranha Plants, malevolent Kirbys, a reformed Wart and a photograph of Princess Peach. Marin and Tarin's uncanny resemblance to Malon and Talon from Ocarina of Time may be the result of the Wind Fish having been around during the events of the previous game, albeit not physically present - perhaps the Wind Fish has Reality Warper powers while he's dreaming?
Whale with lots of power? Sounds like the Ocean King. He could be sleepy from all that fighting against Bellum and needed a nap. This would also mean that cross-timeline traveling is possible for beings of that power, since this presumed to be a sequel to ALttP and that is stated to be Child Timeline.
Cross-Timeline travel? You're heading into Timey-Wimey Ball territory...However, another popular theory is that Link's Awakening is the sequel to the Oracle games (as a sequel to A Link to the Past, but in no way related to Wind Waker/Phantom Hourglass), as in the ending credits of the linked game, Link sails away on a ship suspiciously similar to that in the Link's Awakening opening credits.
Alternatively, because it's a different timeline, Bellum is an Alternate Universe Nightmare, or the same entity with a different name. Basically, it's Links Awakening from the "Adult Timeline" instead of the "Link Dying" timeline. This would also mean that there might be another in the "Child Timeline" if the "Wind Fish, Ocean King" has a counterpart there.
Is there anyone else who could dream up a world with both Zelda characters and Mario enemies?
Yes. Any Nintendo fan. Wait...
The Wind Fish is the personification of every Nintendo fan.
Fans that would die to see a Mario/Zelda crossover. After being woke up, the Wind Fish tried to accomplish this, turning it Up to Eleven, and Super Smash Bros. came to be.
The people and monsters on the island were fake, but based on real people.
It explains the similarity Marin and Tarin have to Malon and Talon. Plus how some characters reappear in the Oracle games.
From the Meta point of view, Malon and Talon were based off Marin and Tarin. In-game, if you take the WMG Timeline proposal from above, it could be that Link was dreaming about the people he met in the Oracle games.
Tarin's transformation is a reference to the leaf and tanuki suit powerups in Super Mario Bros. 3.
This game has several other references to the Mario games, and Tarin has some similarities to Mario, so why not? (So, would that mean that the "it sure was fun" line of dialog was self-promotion by Nintendo?)
The shopkeeper is one of the Nightmares masquerading as a human.
Hence the ridiculously high prices and killing you if you steal anything: he's doing everything he can to stop you from waking the Wind Fish.
Marin was a lucid dream.
There were no real people on the island that disappeared at the end. Everybody was just part of the dream, so that when you wake up, no one's really "gone." The Wind Fish just stopped dreaming about them. Marin, who dreamed of being free and who once tried to go wake the Wind Fish, was a part of the Wind Fish's mind that was trying to wake himself up from the dream. The perfect ending was more symbolic than anything.
The island was Link's dream, not the Wind Fish's.
The entire game is a dream or hallucination by Link as he's floating out at sea, slowly dying of thirst and exposure. Fresh off his last adventure (since Link's Awakening was designed as a direct sequel to A Link to the Past, so it stars the same Link), it's the only thing in his mind to keep him busy as he drifts. This also explains the similarities to the last game even when they don't make sense — for example, there's a castle on Koholint that no one lives in, and what are the odds that both places have a sacred flying rooster? At the end, with the Wind Fish awake, Link dies at sea, alone, but happy.
The Wind Fish is the Zelda equivalent of Azathoth.
How long has been the Wind Fish sleeping? Why can it only wake up to music? Simply, he is an Eldritch Abomination, although not a malicious one. He lies sleeping in the ocean and was invaded by Nightmare. Link, who was traveling the ocean, encounters a storm (in reality, the portal to the Wind Fish's dream) because he is summoned by the deity to help him. Koholint and its inhabitants are simply A Form You Are Comfortable With for Link that got too real. Marin is "real" in the sense that the Wind Fish made her real, probably knowing the fondness of Link for her, and as a thank-you gift for destroying the Nightmare.
Following that, the Ocean King is the Alternative Timeline Wind Fish
It's generally accepted that Link's Awakening goes after A Link to the Past, a game that is accepted to be in the Child Timeline. So, the Ocean King is simply another version of the Wind Fish; both summon Link to their respective dream realms (Koholint Island/World of The Ocean King) to fight a malicious invasion (The Nightmare/Bellum).
Levias is a giant flying whale that serves as the guardian deity of Skyloft. In the child timeline, he just happens to be surfing one day when the Nightmares possess him, and he pulls Link in to help him. Or, perhaps, by that point in the child timeline, Skyloft's been abandoned or destroyed, so he's just a wandering spirit that still retains power, but has no official position. And in the adult timeline, Hyrule is flooded up to around the same level as Skyloft, so he's repurposed from a guardian of the sky to a guardian of the ocean.
Marin may make exactly one wish to the Wind Fish
If you die at some point in the game, then you may continue as normal for video games, but you no longer get the ending where Marin leaves the dream. In this case, it's more than a game mechanic. If Link dies, Marin wishes that he could remain alive. The Wind Fish grants this by allowing Link to survive as long as he wants inside the dream. Unfortunately this uses up Marin's one wish. If you beat the game without dying, her wish remains unspent, so the Wind Fish grants her the wish she wanted for herself: to become a seagull.
The game refers to you as THIEF after stealing because it's Link's own judgment on his morality
Since the game is taking place in Link's dream, we get an insight on his morals. If he steals from the shop, he will make the judgment that he is a THIEF and will take it to the grave because of his guilt.
Hot Head was dying when Link fought him
Hot head (the boss from Turtle Rock) is on fire, and you fight him in a lava pit by shooting fireballs at him. It makes no sense that fire would hurt a fire creature, unless Hot Head fell on the lava pit and was trying to escape when Link found him. However, burning to death would take him too long, that's why the boss is only defeated when Link shoots even more fire at him, accelerating the process.