I did not see your further posts until this afternoon. Bit late, but we use iPhone 8's. Good to read that you have your iPhone's email working. Thanks ITgeek for the Settings info. Wrt your Mac, >> 'on my Mac, I was told ‘This account already exists’, and I could go no further, though the allegedly pre-existing account could not be set up on the Mac)' it sounds as though the Mac thinks that you are trying to set up a new account rather than simply log into your existing account.