Hello,
As per my knowledge, the function keys take their command from the module pool program rather than the standard browser functions. So, the program functions are given preference over standard if both are present. Please make sure your module pool program function keys are working on Desktop IE browser. If yes, it should work on the device too.
Avoid using Cntrl + function keys as it is anyways a tedious task for the workers on the factory floor. Also, in order for them to just press the Function keys (F1, F2, etc), they will have to press the blue button and then the respective number button, as i told you previously for your device.