I am a bit surprised about the first request. On my side, Firefox opens fine when clicking this icon. In the source code, the progam is set to look at the registry at "HKEY_CLASSES_ROOT\Software\Classes\http\shell\open\command", so when the default browser is set at this level, no problem. I have changed it to "HKEY_CURRENT_USER\Software\Classes\http\shell\open\command" instead.
The second one is a lot trickier: Fab's AutoBackup lists the files to copy and recreates all the folders. That's difficult to also list EVERY folder, get their dates AND keep good performance.