Will this work?
Also, is the RAM small enough to fit a CPU cooler aswell?
This motherboard has '4 DIMM slots - DDR3, non-ECC', does this mean that I can have 4 sticks of RAM in total if I wish to buy more in the future?
Yes it will work, and will allow you to install almost any cpu cooler. And yes you can add more memory, but it is recommended to NOT mix and match, if using all 4 dimms it is recommended to used matched sticks from a memory kit containing 4 sticks of ram.
Edit: The recommendation is from most memory manufacturers BTW.