The Man-ape's whose fur and name change in the cold.
The caprivore with piercing teeth threefold.
My adopted kin, for my only true brothers are gone.
They melted to black before history's dawn.
Ask my name and I'll sing of my home.
For no toe have I, nor knee, nor glome.
With monstrous fame of a ghastly sort.
I'm a notorious false report.
You won't get in if a key's what you've got.
Look on the map. The white X marks the spot.
Who am I and how do you know?
The narrator seems to be
The Loch Ness Monster.
The Man-ape's whose fur and name change in the cold.
Sasquatch in warm climates, abominable snowman in cold. (as previously determined by tjbtech)
The caprivore with piercing teeth threefold.
The chupacabra (lit. "goat sucker") (as previously determined by tjbtech)
My adopted kin, for my only true brothers are gone.
Nessie is purported to be a plesiosaur, the last of its kind.
They melted to black before history's dawn.
Her relatives have long since decomposed into oil. (as previously determined by tjbtech)
Ask my name and I'll sing of my home.
Her home is in her name - Loch Ness.
For no toe have I, nor knee, nor glome.
plesiosaurs don't have legs/toes/knees/glomes, they have flippers.
With monstrous fame of a ghastly sort.
Nessie is a monster. Like a ghast, she is difficult to locate.
I'm a notorious false report.
There have been dozens of dubious sightings of Nessie, going back to 1933.
You won't get in if a key's what you've got.
You can unlock a lock, but you can't unlock a loch.
Look on the map. The white X marks the spot.
Loch Ness lies southwest of the intersection of the A9, A82, and A96 roads, which form an X shape.
The Man-ape's whose fur and name change in the cold.
The Yeti or "Abominable Snowman" - snow-dwelling cousin of Bigfoot.
The caprivore with piercing teeth threefold.
Chupacabra - literally means something like "goat-sucker" and leaves three teeth marks when sucking blood from animals.
My adopted kin, for my only true brothers are gone.
Zombies, mebbe?
They melted to black before history's dawn.
I think this must be referring to prehistoric creatures, such as dinosaurs, going extinct and becoming petroleum and coal.
Ask my name and I'll sing of my home.
I'm not sure but could be the Sirens..?
For no toe have I, nor knee, nor glome.
Ghosts - non-corporeal entities.
With monstrous fame of a ghastly sort.
Scary monstros, like vampires and mummies, in movies (or hiding in the closet).
I'm a notorious false report.
UFOs - "swamp gas," etc...
You won't get in if a key's what you've got.
Heaven?
Look on the map. The white X marks the spot.
X-Files - title screen/logo has a white "X."
...Final answer:
I suppose you're the paranormal.
[EDIT: After adding explanations for the fourth and fifth lines, I'm wondering whether the answer must be made more general - changed to the unknown.]
[EDIT: A couple of my line explanations might be dubious, still.]
