Re: Add or edit my sign-in email : It will not allow me to add my current address and remove the old one.
Once you setup an Apple ID with the "@icloud.com" email you cannot switch to 3rd party email.
or
If someone else is using a particular email address as their Apple ID you will be unable to use that same address.
Else:
See Apple support's online article (link below) for how to change your Apple ID to a different email address:
Change your Apple ID - Apple Support
If needed: How to: Get a verification code and sign in with two-factor authentication - Apple Support