Of course. Set the patterns that you require and set the mode to "Proxy by Patterns"

Badges are per tab and if a tab uses a proxy, it shows. Some tabs are loaded from the browser cache and there were no net-requests made from that tab.
However, if there is an issue, please post the details to the support for further investigation.

The server list is an auto-fill helper to fill type, hostname and port. Extensions do not have direct access to other applications running on users computer.