Using New Outlook on Windows for personal email, calendar, and contact management
I'm sorry the new Outlook has been one problem after another for you, Jeff White.
One thing I think might be related to all three of your problems is that Microsoft is currently experiencing a service issue, affecting Outlook and other Microsoft 365 services. Many people are unable to access their emails, sign in or use some features at the moment, including "Google quota issue" similar to what you're facing.
The new Outlook gets your Gmail through a Microsoft connection, whose trouble can affect attachments and saving. Google limits how many sign-ins it accepts from Microsoft's app, and the limit sits on Microsoft's side, not your Google account. There's likely nothing wrong with your account or your PC.
Each new sign-in attempt runs into the same limit, so for now, use Gmail in your browser. Once the service issue is fixed, open Outlook and sign in to Google when it asks > select Allow on Google's permission page. You can also follow Microsoft's updates on the service status here:
Once the service issue is resolved, if Gmail still won't connect, or attachments still won't open, reply here and we'll go through it with you step by step.