Attunement rules state that a character can only be attuned to three different magic items. Is the Attunement aspect of a magical item evident to the identifier? Is this intended to be knowledge about magic that a character is aware of? Or is this meta-knowledge for the mechanics of the game (like, a character isn't really aware of how many hit points they have)?
Identifying an item tells you if it requires attunement
There are two primary ways to identify a magical item. You can use the identify spell, which explicitly clarifies that you know if an item so identified requires attunement. Alternatively, you can take a short rest while holding and focusing on the item, at the end of which the character "learns the item's properties, as well as how to use them" - which must also mean that you know if it requires attunement, because that's a property of the item and if attunement is required that is part of knowing how to use the active properties.
The mechanics of attunement are not abstract and can be easily determined in-character, so are reasonable in-character knowledge
The Identify spell tells a character if an item requires attunement. Resting and meditating upon an item necessarily tells the character if it requires attunement. The rules for attunement describe that the creature is making a deliberate effort to try and attune with an item in order to use it. Clearly, the ability/requirement to attune with certain magical items can and must be in-character knowledge. Further:
An item can be attuned to only one creature at a time, and a creature can be attuned to no more than three magic items at a time. Any attempt to attune to a fourth item fails; the creature must end its attunement to an item first.
A creature can also voluntarily end attunement by spending another short rest focused on the item, unless the item is cursed.
Though a given creature may not know enough about magic to know that they can only attune to three items at a time, the rules mandate that attempting to attune to any more items automatically fails unless one of the existing attunements is broken, which again requires deliberate, in-character action on the part of the character (or other non-meta requirements to be met, like losing the item for long enough or someone else attuning to it). It would not be difficult to infer the 3-item limit by experimentation if you had enough magic items to hand.
You would expect that any creature with magical knowledge could know this rule of magic (I'd make it very easy Arcana check if I was even inclined to call for a roll), and any half-way intelligent creature could work it out by experimentation. The limit is a definite, "real-world" value, not an abstract quantifier like XP or hit points - it doesn't make sense, with the mechanics described, for a character not to be able to understand they can only attune to three items at a time.
Answering the title question:
Yes, identifying a magic item reveals it requires attunement
Identifying a magic item reveals all of its properties, unless the item, or the property, states so. An example of property that does state it is not revealed is the Cursed property (DMG p. 139).
Most methods of identifying items, including the identify spell, fail to reveal such a curse
Note that you can attune to an unidentified item, and attuning to it does not reveal the properties. See Sage Advice.
The Identify spell explicitly states
If it is a magic item or some other magic-imbued object, you learn its properties and how to use them, whether it requires Attunement to use, and how many Charges it has, if any.
Short resting to identify the item is supposed to do the same thing as the Identify spell. See Sage Advice 2. Although it's unclear what Crawford means with "more information". There is opening for saying that short resting is not enough to learn about attunement, imo.
The other methods of identifying an item (experimentation, for example) do not reveal all of its properties, though, so they are up to the DM to say if it reveals the requirement of attunement or not.
About the body questions:
Similar to how characters don't know how many HP they have, but they do know how hurt they are, how close to dying/fainting they are, etc., they might not know what exactly is attunement, but they do understand the concept - that some magic items require some magical special bond, and you can't bond to more than 3 at a time.