I just got a NUC6i5SYK to use as a home theater PC for my movies, so the only thing i can comment on is number 1.
The new NUCs don't have HDMI 2.0, so you can't do 4k @ 60Hz, unless you try to go through the mini DisplayPort.
From the technical manual:
The maximum supported resolution is 3840 x 2160 @ 30 Hz and 2560 x 1600 @ 60 Hz, 24 bpp (WUXGA). The HDMI port is compliant with the HDMI 1.4b specification.
The maximum supported resolution is 3840 x 2160 @ 60 Hz, 30bpp. The Mini DisplayPort is compliant with the DisplayPort 1.2 specification.
Do *not* buy Corsair ValueSelect for your NUC6. Here's a thread I created about problems that were eventually connected to my RAM: NUC6i3SYH Random freezes
I'd recommend getting Kingston HyperX, which have been working for both me and some other people in that thread.
Thanks Johan, that thread is exactly why I asked first.
I was going for this memory until I seen that thread, not exactly the same model?? but might be just marketed differently
I don't know about the Corsair Vengeance, nobody has mentioned them as either working or not. The ones who reported the same problems as me specifically said they had ValueSelect.
Kingston HyperX works for me, while someone with Kingston ValueRAM had problems which sounded memory-related (only 1 report though so it's a bit of speculation). Could be that budget sticks (ValueSelect / ValueRAM) have more issues than the premium lines (Vengeance / HyperX) but it's just a guess.