Getting notifications that I’ve been hacked and now can’t receive Gmail emails on my iMac

Those aren't messages, they're notifications.

A site you visited has given itself permission to send push notifications. Everything you're seeing is nothing but a scam.

Open Safari's preferences. Click on the Websites tab and then scroll down to Notifications. Clear any entries in the right hand window. You might find something similar in the Pop-up Windows heading below that. Block any you don't recognize.

Then if you want, uncheck the box on the right, as shown below here.

I personally can't think of any reason why I would ever want any website to push notices to me.

Delete the Gmail account on your Mac. Don't worry, this is only a link to your account. Your emails will still be on Google's servers.

Then create a new Gmail entry, using your account name and new password.