For the case and cooler:
From the specs: "CPU cooler height: 155mm / 6.1 inch"
The cooler height is 158mm. Your call
I've found that the case dimensions are usually pretty conservative. My Antec One lists max cooler height at 155mm, but a 159mm CM Hyper 212 Plus fits with 3mm clearance, even discounting the side bulge.
It may or may not fit.