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