> Function keys are inverted by default and I have not established how to flip that at a system wide level

Not sure about this specific Lenovo laptop, but if anyone else is having a similar issue on a Lenovo, I'd suggest checking the BIOS settings; my Ideapad 700 had a setting there called something like "legacy function keys", which made the function keys act like function keys by default (and required using the "Fn" modifier key in combination with a function key to change the backlight, volume, etc.)