Keep my Apple ID, but delete individual iCloud services and data (for example the mailbox @icloud.com)

You can't remove the email functionality from a icloud.com or me.com adress. What you can do instead is to

• log into icloud.com in any browser
• go to Mail
• click on the cog wheel at bottom left and select Settings (first entry in the menu)
• set auto-forwarding of all mails to your new email adress

This is impossible as clearly stated on Apple's website:

How to change your Apple ID if it ends with @icloud.com, @me.com or @mac.com

If you use an @icloud.com, @mac.com or @me.com email address as your Apple ID, you can’t change it to a third-party email address.

That is your Apple ID so you can't change it, the only real alternative is to create a new Apple ID.