Xbox Live: How do I switch from a hotmail email to an outlook email on my account?

Unfortunately this is not possible and since your email is a Microsoft email (Live, Hotmail or Outlook) you can't switch the email to another one and have the account not be connected to that email anymore, technically.

You can switch the login emails around but you CAN'T switch TO a Microsoft email when you do this (Live, Hotmail or Outlook). You can switch to another email provider but you can't switch between Microsoft emails as they're permanently connected to that
account they were created on. For example, you can't switch this account's email login to another Microsoft account because that email is attached to a Microsoft account already.

The only solution is to start over and have him create a new account and have the account that owns all the games to be set as the my home xbox account on the xbox one so that the new account can play all the games that account owns BUT the saves and any
progress will not move over and some DLC will not share, also.

https://support.xbox.com/en-US/games/game-setup/my-home-xbox

Since outlook is already a Microsoft server email it is not possible to use the outlook email you can add another email alias that is not a Microsoft server email (@outlook.com, @live.com, @msn.com) or you can create a new outlook email in the process of
adding an alias to the account at account.live.com/addassocid and it will put that new outlook account on the hotmail account or you can use any non MS email account.

Now keep this in mind you can have multiple aliases that you use to sign into accounts with (if they are not already a Microsoft account)

If you do add a new alias to your hotmail account and decide to remove your hotmail email from the account that will render the hotmail account null and void and you will never be able to get it back.

so do not remove the hotmail email from the account if you ever think you will need it for anything in the future

Ok, so if i create an alias and i remove my hotmail email i will not be able to use the hotmail email, but will i lose all the data and achievements of the xbox account? (i hope not...)

please note that if your email address is a Microsoft email (@live, @outlook, @hotmail, etc) it can't be removed from an Xbox account

Since outlook is already a Microsoft server email it is not possible to use the outlook email you can add another email alias that is not a Microsoft server email (@outlook.com, @live.com, @msn.com) or you can create a new outlook email in the process of
adding an alias to the account at account.live.com/addassocid and it will put that new outlook account on the hotmail account or you can use any non MS email account.

Now keep this in mind you can have multiple aliases that you use to sign into accounts with (if they are not already a Microsoft account)

If you do add a new alias to your hotmail account and decide to remove your hotmail email from the account that will render the hotmail account null and void and you will never be able to get it back.

so do not remove the hotmail email from the account if you ever think you will need it for anything in the future

Ok, so if i create an alias and i remove my hotmail email i will not be able to use the hotmail email, but will i lose all the data and achievements of the xbox account? (i hope not...)

You will not the only thing that you would be doing is changing the email address that you use to sign into the account with.

I am trying to change the address from a Hotmail account to a gmail account, is this possible?

Yes, you can change TO any email address that is not Hotmail, Outlook nor Live mail. You just can't change TO one of those emails - as they are permanently connected to microsoft accounts.

You can switch any email to a Gmail just fine.