Welcome and congratulations!
The F logo shows up when you are in manual mode and choose the gear position page of the multi-function display, or whatever it is called.
AFAIK, there is no way to run the fogs without the low beams. There may be some sort of mod out there, but I've haven't looked for it.
Enjoy your new F!
Jeff
08 Smoky Granite Mica IS-F