Your screen shot shows the primary mail address signed in www.icloud.com is example1@me.com and secondary mail address added as example2@icloud.com
And as per the article Create an email address for iCloud Mail - Apple Support
Note: If you set up iCloud using an Apple ID that ends with @mac.com or @me.com, you don’t need to set up an @icloud.com email address to use iCloud Mail. You already have an equivalent address that ends with @icloud.com.
So enter with account credentials at appleid.apple.com and remove the mail address example2@icloud.com see the section - Delete an additional email address in the article About your Apple ID email addresses - Apple Support
You can add gmail account to iCloud .
Create a gmail account on the web https://support.google.com/mail/answer/56256?hl=en
And add in Mac system preferences > internet account Add an internet account - Apple Support
Use your Internet accounts on Mac - Apple Support
Change Internet Accounts preferences on Mac - Apple Support
You can also create a new Apple ID using gmail address from www.icloud.com see the web account section in the article How to create a new Apple ID - Apple Support
When gmail account is set in Mac and configured with iCloud you don't need to manually add port settings , even you try to add it won't keep all as empty .