With a 2666 motherboard? Actually, yes, but it's not the maximum performance you can get out of it. It's best to check the motherboard manual to see if 2133 works (there are always peculiarities), but I'm leaning towards a 99% "yes".
No. You need DDR4 SO-DIMM RAM and not DIMM. For example, the following products:
Corsair Vengeance SO-DDR4 (1x, 8GB, DDR4-2400, SO-DIMM 260 pin)
Corsair Vengeance SO-DDR4 16GB 2-Kit (2x, 8GB, DDR4-2400, SO-DIMM 260 pin)