Theres Programs that allow people to autoclaim tags once they get freed up

If a person doesn't sign into their Xbox account in 5 years, the tag will be freed up for use. However, since the account can be used on multiple Microsoft services, there is no way to know exactly how inactive an account is. Also, since they now allow duplicate gamertags, there are already multiple people using that tag. So even if the original is freed up, you would still be given a suffix to differentiate you from the others that have the tag.

No. Mass resets were discontinued a while ago. If a person doesn't sign into their Xbox account within 5 years, the gamertag will be freed up. If they don't sign into their Microsoft account within 2 years, that will close the account and should free up the tag as well. Otherwise, with the system allowing multiple people to use the same tag now, it may be hard to get some of those gamertags.

The only way to get it is if the original owner changes the tag or it gets freed up by the system and nobody else uses it before you get it. There's no way to request it to be freed up.

If the gamer tag is in use, you cannot request it be freed up. People have microsoft accounts they use for many things, and all MS accounts have tags attached.

Once a gamertag is released, you would just change your gamertag like you normally wound. If it's freed up, you'll be able to change it to that tag.