hi, the security essentials signature update are not handled through the browser but to the windows update mechanism built into the operating system. so this is a problem that won't be related to firefox and where we are unable to give advice. please get in contact with microsoft's support at https://www.microsoft.com/en-us/safety/pc-security/troubleshoot-updates.aspx to get help about this instead. thank you for your understanding!

The Windows Updater program uses Win IE to connect to Microsoft. Microsoft doesn't allow any other browser (as far as I know).