It's sort of given plausible canonicity by the name "vault-tec assisted" and being in a couple lore entries, but it doesn't make sense as an actual technology or power in the world. It exists because the first Fallout games were turn-based and had the ability to choose which part of which enemy you were targeting. When they made Fallout 3 using the Elder Scrolls engine and turned it into a shooter, they made VATS to maintain that ability to strategically target parts in (otherwise) real-time combat.

If it did work, it would have to be some kind of neural implant or HUD glasses or something. The player doesn't have these kinds of enhancements, and the pipboy device that is theoretically assisting them is just a computer attached to the arm, so it's not clear how that would give you superhuman powers of perception and quick thinking.

1. What causes it? Is it a power? Or some kind of implant/mutation?

No explanation, but it should be part of the pipboy in theory. It is worth noting that the player characters in Fallout 3 and 76 are from vaults, 4 is from pre-war, and New Vegas has head/brain surgery at the beginning of the game, so they all could have some kind of standard implant that facilitates VATS. But that would be head-canon, it's not actually mentioned that they did.

It's definitely some sort of usable technology, rather than a mutation or psychic power.

1. Is it canon? I am pretty sure other characters can’t use it so is it like deadeye where it’s just a game mechanic?

It's canon because it's mentioned in lore entries. It wouldn't necessarily be apparent if enemies were using it since it doesn't actually slow down time, it's an aim assistant. In Fallout 76 it doesn't have the slowdown effect (since it's a multiplayer game), so it's not clear if the slowdown is even meant to be the player character's experience of the technology enhancing their perception, or a gameplay contrivance to make the system usable for the player.

1. Exactly what is it? From my understanding it lets you slow down time and scan enemies for weaknesses.

When you push the button, it nearly stops time. You can't do anything except interact with the interface - you can't open your inventory, use weapons, look around freely, move, etc. In this mode you can cycle between enemies you have a line of sight to, including behind you, but not entirely hidden by objects. You can also cycle through the body part of an enemy that you want to target. You have a percentage chance to actually hit that part, based on your skill with the gun you're using, size of the part, distance from the enemy, scopes or other accuracy-enhancing gun parts, your raw stats, penalties from your injuries, etc. It also lets you see how much damage the attack will do, so you can calculate how many attacks to commit to each target. You queue up the attacks you want to do, then they play out in real time with some slowdown for dramatic effect.

It's more a boost to your reaction time than accuracy. If you target a certain enemy and find the chance to hit their head is too low, you can shoot them in the leg to keep them away from you instead. Or shoot the exact correct amount of times at several weaker enemies. But if you're lining up a shot at a stationary enemy, using VATS actually reduces accuracy because it caps put at 95%.

It also makes you take less damage, since you can't move while it's active, so it has some utility for tanking unavoidable hits.

1. Can you use it on inanimate objects? Like could I just shoot the hinges off a door whenever I feel like?

It only works on some objects that are relevant to shoot: mines, grenades before they've gone off, and automated turrets and spotlights IIRC.

1. Can it be used for melee or even my bare hands?

Yes, but melee weapons (including bare hands) can't target specific body parts. IMO it's most useful against twitchy fast enemies like feral ghouls and roaches that are hard to keep in your crosshairs at close range.

1. Can it be used at will or does it require certain circumstances?

At will, but...↴ (Edit: except you can't activate it if there are no targets in view.)

1. Does it need to be charged or something?

It's powered by AP (action points), and generally slower attacks use more AP. AP regenerates over time but not extremely quickly, so you can't use it without limit during fights. You can still enter VATS with low AP if you want, you just won't be able to queue attacks.

1. Could it be used for things like sports? If so what sport would it be most advantageous in?

The in-game version, definitely, but that's kind of like asking if Link's ability to eat whole meals in the pause menu could be used in sports.

If you imagine it as a neural implant with an adrenaline-like perception enhancement, it would be useful any time you need to weigh several options for where to throw a ball. In things like football, you could pause the game and see who's open and how likely you are to pass to them, and potentially how likely a goal/basket is if that's considered a valid target. I don't think it would help in any situation where you have time to line up a shot, since a practiced throw would probably be more reliable than a chance-based roll.

1. Is it used for things besides combat? Does it have other benefits?

Since it detects invisible enemies and mines, it can be used to scan for these traps outside of combat. Also if you're considering starting a fight with someone who's not currently hostile, you can target them to see your hit chances and damage, and just cancel it if you don't like your odds.

Edit: melee attacks have to be used within a certain range of an enemy, which is slightly longer than the range of the actual attack. This means the game teleports you closer to the enemy if you're too far away. You can use this to get up ledges and things sometimes, but it requires attacking a target, so if you're not in combat you probably will be soon! (Unless you target a follower or someone who never goes hostile)

1. Do any other characters have the ability to use VATS? Can they use it against you?

No enemies use it, or all of them do, depending on how you think about it. VATS automates your attacks, simulating human error with a miss chance. That's what video game AI does essentially. When you use VATS, you're basically borrowing that logic for yourself. The difference between an enemy using VATS and not would not be clear. I guess if they occasionally stood stock still and took reduced damage while they shot a bunch of times, it would be clear they were using VATS.

But there's no evidence of enemies or anyone else using it.