In response to your first question regarding whether or not you could purchase two more memory sticks to completely fill the slots, the answer would be "Yes". Gaming rarely utilizes more than 8GB of RAM, but if you desire to upgrade to 16GB of RAM or more, you could and it wouldn't hurt. Just when you install the RAM, the RAM slots on your motherboard are usually color coordinated to designate the different channels. For example, The motherboard on my computer has blue RAM slots for the first channel and white RAM slots for the second one. If you are installing the RAM to utilize the dual channel RAM, put one 4GB module in a blue RAM slot and the other in a white RAM slot. The manual that came with your motherboard should further explain the exact configuration of how to install the memory slots if needed, But, To add an additional two modules to the system while still utilizing the benefits of dual channel RAM, such as higher bandwith, It would just require that whatever RAM you have installed in the first channel matches what you have installed in the second channel. Whether that be 4GB and 4GB, 8GB and 8GB, and so on.
In response to your second question about the Hyper212, As long as you stick to a low profile brand of RAM that doesn't have a huge or tall heatsink on it, you should be fine. I would agree with the previous poster that Crucial Ballistix Sport makes quality RAM with solid 9-9-9-24 timings that are reliable and fast. I would generally stick with DDR3 1600 for right now as DDR4 is just way too overpriced yet and you won't be able to utilize the full benefits of the lower power consumption or higher bandwith of DDR4 yet as we have a hard enough time even technologically utilizing all of the benefits of DDR3 just yet. GSkill Sniper, GSkill Ripjaws, and Corsair Vengeance all have large heatsinks which could interferre with you installing either RAM or additional RAM. I would again stick with the Crucial Ballistix Sport as a mainstream, low-profile alternative that is compatible with a large majority of systems that can be more commonly found at a cheaper price than the alternatives you previously listed as potential possibilities.
If you have any additional questions or require more information, feel free to send me a private message and I will be more than happy to help. Have a great day!