Gmail

iCloud works only with its own addresses. You can't use it to connect to another service. You can set up GMail in your Mail application using the settings they provide.

You could read your Gmail messages in the iCloud Mail section by forwarding them from Gmail, but you can't answer with the GMail address as the 'From' address, only the iCloud one, which limits its usefulness.

If you want to use a gmail email address in signing into iCloud, you will need to change your Apple ID so that it uses that address. I suggest going here to change your Apple ID: https://appleid.apple.com/#!&page=signin But, before changing it, read:

Changing your Apple ID: https://support.apple.com/en-us/HT202667

and

What to do afterwards: https://support.apple.com/en-us/HT204071