For instances with anonymous access enabled, you can force user authentication when creating the feed by checking 'Authorised'. If anonymous access is disabled, all feeds will require user authentication.

You must append a valid login to Private Feeds as described in the Usage section of the RSS Feed Macro.

The URL is invalid. If the link appears correct, confirm that you can access Confluence. Paste the feed into a third-party RSS feed reader and confirm that it can access it. If it cannot, your firewall settings may be blocking access to Confluence. For example, your server may be configured to block outgoing requests.

The feed source may be offline, or the firewall may be blocking access either between the Confluence server any your computer. Confirm that you can access the feed URL from your browser. If it cannot, your firewall settings may be blocking access to Confluence. For example, your server may be configured to block outgoing requests.

The link is not a valid feed, so check your URL. If stuck, you can recreate internal Confluence feeds Using the RSS Feed Builder.

This is not possible, but you can vote towards tagging incoming mail with labels on arrival. Once tagged, feeds could monitor all new mail with that label.

No, as RSS feeds are based on the view permissions for pages and spaces. RSS is an extension of normal page viewing functionality, so if you can view a page, you can receive an RSS feed for it. The only way to remove the an RSS feed is to prevent all access to a page for that user, so no content will be delivered.