It sounds like you're facing two separate issues with Outlook synchronization and the Dynamics 365 App for Outlook installation.
1. Outlook to Dynamics 365 Sync Issue:
Make sure you have configured server-side synchronization in Dynamics 365 for both incoming and outgoing emails. You can verify this by going to Settings > Email Configuration > Mailboxes. Open your mailbox record and ensure that incoming and outgoing email settings are enabled.
Also, check the Personal Settings in Dynamics 365 under Email and ensure your email settings are configured to track emails automatically, especially for emails sent from Outlook.
Make sure your Dynamics 365 security role allows for "Track in CRM" permissions.
2. Error Installing the Dynamics 365 App for Outlook:
The error code -2146863614 and mention of a missing CAB file often indicate that a required solution file (AppforOutlookAnchorSolution) isn't installed or there's a problem with the version you're trying to install.
Go to Settings > Solutions in Dynamics 365, and confirm if "AppforOutlookAnchorSolution" is listed. If it isn’t, you may need to download the required CAB file or solution package from the Dynamics 365 Solutions library or contact Microsoft support to obtain it.
Once downloaded, you can try manually importing the solution from Settings > Solutions > Import.
Let me know if these steps help or if you need further guidance!