To turn off your antivirus just right click on the icon in your system tray, it should give you the option to disable it temporarily, or turn it off completely. As far as your browser is concerned, I'm not sure if it would make a difference, but it would be an easy thing to test, and wouldn't cost you anything.
edit: I see you figured it out. You may still want to visit the logitech forum and ask if anyone has some settings that would allow firefox to work, but then again for as often as you likely need to update the remote, it's not really that big of a deal to use IE.