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1. Aside the clock speed difference, the processor numbers for the 3rd generation Intel® Core™ processor family have an alpha/numerical identifier followed by a four digit numerical sequence (3xxx), and may have an alpha suffix depending on the processor. The main difference for “K” series is the clock multiplier on the 'K' processors is fully unlocked, allowing for very high overclocks. On the 'non-K' versions, you may only change the turbo-mode multiplier which will allow for slightly higher clock rates when less than all 4 cores are active.
2. This is a really hard question, but to give you an idea please access the following link http://ark.intel.com/compare/65523,70845
I did a comparison chart so you can see the specifications of the i7-3970x vs i7-3770k, so you can take your own decision, since Intel® doesn’t benchmark our processors, we cannot give you a detailed explanation how better is one of these processors than the other.
3. To give an idea, i7-3970x is a Sandy Bridge platform with 2011 socket, based on 32nm lithography and it is for extremely heavy applications like server environments, and the I7-3770k is a Ivy Bridge platform with 1155 socket, based on 22nm for desktop computers. Any of these processors are really powerful and will meet your expectations.
About the PCIe 3.0 rev. gameplay performance advantages are under 10% over PCIe 2.0 rev. so it will not change the actual gameplay experience, nowadays but maybe will take a huge advantage in the future.
At the end is your own decision what processor to get, but for gaming purposes the I7-3770k processor will meet all your expectations, and remember that at the time you get a external video card, it will be in charge of all related graphics processing, so make sure you will get a powerful video card as well.