Are the schools of magic presented in The Elder Scrolls defined by mages/the people who make use of them, or by some higher law? Like, who says, "Okay, so Levitation will be Alteration"?

They seem to be defined by what their effect is in the world. Alteration "alters" material things in the world, Illusion changes our perception, Destruction destroys things etc. etc.

But what about things that are more ambiguous? Like absorption spells, which damage the target's abilities or health/magicka/fatigue and restore yours at the same time, could seemingly be either Restoration (which they are) or Destruction. Or Levitation like before, which really seems more of a transportation type of thing, in which case could seemingly belong under Mysticism.

There's a good deal of argument among in-game mages over which spell effects belong in which schools, even when the classification is seemingly unambiguous. See for example http://www.imperial-library.info/obbooks/response_bero_speech.shtml.

Like real world scientific disciplines, the Schools of Magic in Tamriel are constantly being anolyzed, debated and restructured.

A good real world comparison is the classification of plants and animals by species, genus, etc. This has been revised heavily several times.

Magic is no different. In one game Absorb Health may be Restoration, but in another it may be Mysticism. Scholars, Battlemages and Wizards will continue to debate and revise these classifications pretty much forever.

You should understand that the skills used in game are a game mechanic only. In a "real" world setting, casting Heal over and over isn't going to increase your knowledge of absorbing attributes from a foe. Ignoring the limitations of the game engine, every spell pretty much stands alone and must be practiced individually to perfection by the most powerful mages. Magic is magic. The only true variation is the source of said magic. Some is channeled through a person's body. Some can be a blessing laid on by a deity or artifact. Others come from potions and magic gems. But it's the same type of energy whether it's used to heal a cut across a soldier's leg or to blast a skeleton into smithereens with a fireball.