For backing up your email from gmail or any other provider, check out MailStore Home edition: https://www.mailstore.com/en/products/mailstore-home/ It will grab everything in the account and store it locally, and then allow you to push it back onto any other imap service when necessary. Great for migrating your email, and keeping a just-in-case backup.

Email is the one thing I have stopped trying to do myself. It just has too many things that you absolutely need to keep updated. Have a look at Forward Email (https://forwardemail.net/en). They can hook up to pretty much any domain setup you already have, and do the heavy lifting for you.