the only issue i have with stock cooler is the plastic legs that can weaken or fail over time. your better off spening a few bucks picking up a 3 party cooler that uses a back plate and screws.
Your CPU NEEDS a cooler. I believe that the newer skylakes do not come with a cooler and you need to purchase one separately.
You can mount fans in your case in any orientation to make them either an intake or exhaust fan. As the guy before me said, generally top and rear are exhaust and bottom and front are intake. But you can do it however you want.