1. Bandwidth measurement.
Open "Tools" menu and click the item "Bandwidth Meter". You can perform upload and download bandwidth measurement. It also shows your public IP address and public domain name.
2. Broadband troubleshooting.
When Firefox fails to load a webpage, the extension will automatically check whether Internet connction is working or not. You can perform further diagnostic tests (ping, traceroute) or check the archived version of the failed webpage. Just try to type a non-existent domain name(e.g., qwqwqwq121212.com) to see this in action ...
Note: if you use windows, you may use a more advanced version that can perform windows specific diagnosis. See https://addons.mozilla.org/en-US/firefox/addon/2360