As stated elsewhere, you'll need to download the drivers from Intel (Drivers & Software), put them on a memory stick and install them in Windows. Install all of them, not only the network drivers. You'll need a separate PC to get these drivers. If I were Intel I would have included a 50 cent memory stick with their logo and those drivers on it in the box, charged an extra dollar for the NUC and everybody would have been happy. Would have looked so much more professional. But alas, I am not Intel :-)
The buggy behavior in getting into the BIOS with F2 is something that baffled me also; it was very annoying. The good news is, ever since I 'finished' my Windows 10 installation (stopped installing drivers, upgrading the OS etc. with every reboot) it went away and now I am able to enter the BIOS without problems.
EDIT: Re-reading your question: I could not get my NUC to enter the BIOS using a wireless keyboard (Logitech with unified tranceiver) at all. Use a cabled keyboard.