Maybe. If you could finally tell me which settings you're going for in games I could tell you if it's worth reusing the GPU.
Yes. To make it even clearer: Overclocking Intel CPUs does not improve price/performance, only performance. For AMD CPUs it's free anyway and you can decide later. SLI/XFire do not improve price/performance or performance most of the time because most games don't support them (or only nominally support them). Watercooling doesn't improve price/performance or performance either. Zen hits a wall way before cooling cooling becomes a problem if you're not going for "I'm going to run this benchmark 3 times then the CPU dies"-voltages and Intel CPUs should be delidded when cooling is a problem, which is far more effective and cheaper than watercooling.
So I will ask again: Do you want (or "need") any of those?
Depending on the settings overclocking won't help because you'd be limited by the GPU (except in TF2) and more cores would be cheaper for streaming.
The 4670 uses DDR3, any new CPU uses DDR4. It doesn't matter which sticks they are, if you've got an i5-4670 I can guarantee that they will not work with a new CPU.