Connections established on startup - Firefox
From MozillaZine Knowledge Base
The following is a list of all connections that Firefox may establish at application startup and how to stop them.
- A loopback connection (to IP address 127.0.0.1) on non-Unix machines . The browser is communicating normally with itself, and it is not recommended this be blocked.
- Loading Live Bookmarks. Deleting all Live Bookmarks will stop these connections.
- Checking for application updates. "Tools -> Options -> Advanced -> Update" provides options to disable update checks.
- Loading home page. Setting the homepage to a blank page or a local page will stop this connection.
- Updating phishing sites database. Setting browser.safebrowsing.enabled to false in about:config will disable this feature.
- Prefetching links if the page it's on defines any. See the Prefetch FAQ and network.prefetch-next for further information. To disable pings in prefetched links, see browser.send_pings.
- Updating the Add-ons Blocklist. Setting extensions.blocklist.enabled to false in about:config will disable this feature.
- Updating metadata for installed add-ons (described here). Setting extensions.getAddons.cache.enabled to false in about:config will disable this feature. 
- Firefox Health Report data. 
- Firefox makes unrequested connections (Firefox Support)