Elder Scrolls Lore
This passage is for people wanting to know a little bit about Skyrim lore.
Skyrim is the 5th official game in the Elder Scrolls series (I do not count the other games and spin-off novels and such)
The Elder Scrolls is situated in Tamriel in a typical Medieval fantasy setting (So you will find orcs, elves, and dwarves). Skyrim is a northern province. Its inhabitants, the Nords, are obviously using Viking as a reference. The Redguards are using the Arabic culture. The Imperials, Rome.
In the game, Skyrim the ancient God Alduin, The World Eater, a dragon of immense power is coming to Tamriel and precisely Skyrim to... destroy the world. He is helped by an army of immortal dragons he is raising. Unfortunately for Him a powerful warrior, the Dragonborn, a warrior who can absorb the souls of the dragons, thus killing them will rise against him.
You have one thing to see when talking about the Elder Scrolls in general: The mythology behind the Elder Scrolls is the Elder Scrolls. First and foremost this is what is followed and nothing else. That is to say that Skyrim is, yes, "Norse", but "Norse", is much more a general "feeling" than following "Norse" mythology.
You have also to see that the Elder Scrolls are taping, vastly, in way more things than "Norse". The Imperials are following the Roman empire, seated in a Medieval period. The werewolves are inspired by the modern representation of the modern beast; etc.
I will illustrate, here, how "Norse" will taint Skyrim:
- In the opening sequence, on the cart, you meet a "horse thief" named "Lokir of Rorikstead". Anyone knowing the Norse mythology will see an amusing reference to Loki, father of Sleipnir (Odin's horse) and god of deception (thievery).
- During the companion quest you try to put back together the shattered mythical axe Wuuthrad, that is fairly clearly inspired by the shattered sword of Sigurd/Siegfried Gram.
Note also that: Broken weapons are not especially Norse stuff (think about Narsil in the Lord of the Ring). I still do believe that both Lokir, and Wuuthrad are "referencing" Norse things more than anything else.
Now regarding your specific question. Alduin is a legendary dragon. In term of myth, dragons, malevolent one, as Alduin, are omnipresent. Example: Tiamat, in Mesopotamia, or Apophis in Egypt. Notice both those dragons are as close reference to Alduin as the one I am giving you:
Niddhogr is a giant dragon that eats the root of the World tree Yggdrasill. Niddhogr is completely as malevolent as Alduin, both are god-like creatures. Both are trying to put an end to the world.
As everywhere in the Elder Scrolls, what matters to them is the "Elder Scrolls' lore first and foremost. In the case of Skyrim, this lore is tainted all over with Norse mythology. But it is only a far taint (rightfully). You will not see Odin, Fricka or Valkyries entering the Elder Scrolls pantheon. so don't expect the Elder Scrolls lore to fit the Norse mythology. They just bring some "Norse mythological elements" to have this little Norse feeling in the game.
The Volsunga Saga This is where Gram the shattered sword is found
Norse Mythology by John Lindow
Poetic Edda by Snorri Sturluson