#1412
AiO water coolers are terrible. High end air coolers are better. A custom water loop would be better but isn't even close to being within your budget. It'd also be a ton of work.
3000 MHz RAM is a bit overkill.
The CX600 isn't great, i'd get this one or if you want a semi modular PSU this one.
#1413
I don't think he meant a custom loop, it's not really possible with only 630€ total budget anyway.
#1414
First things first: There isn't much point in doing the exact part list in advance since prices will change. So I'm just trying to get a general idea now and figure out how performance you need. Then you post again in the week that you'll actually build it and I'll make the part list with the current prices.
Now about performance. Right now more than 4 cores hardly ever help in games. In fact because the 6850K is Broadwell, which is slightly slower than Skylake and also lower clocked than the 6700(K) it will actually perform worse in most games. In other words it's a waste of money for gaming.
How sure are you about streaming? Because if you won't then even the 6700K is more than you need. An i5-6600K would do just fine. You still have a few weeks to think about that.
Similar story with overclocking. Except you do get better performance in all CPU limited games. However you actually need to overclock. If you buy a Z170 mobo, a cooler and a -K CPU but then don't overclock it you've paid around 200$ for something you're not using.
A 6700K shouldn't be a problem with your budget but I like to mention these things anyway. 200$ are 200$, not some pocket change.
Now about the GPU. Apart from TF2 and CSGO which games would you like to play and how many fps on what settings and resolution do you want to get? That also brings us to the question what kind of monitor do you want? 144Hz? IPS? 1080p or higher? Lightboost? GSync/FreeSync?
It's generally best to get a GPU that does what you want it to do and just get a better one a few years later when you actually need a better one. To buy that kind of performance now you'd pay a massive premium. The GPU market moves so fast that buying a 300$ GPU now and then another 300$ GPU in 2 years actually gets you more performance than buying a 600$ GPU now. That's why you should just get the cheapest GPU that exceeds your requirements. Which obviously means you have to figure out what those requirements are.
About SLI / CF: It's generally recommended to get a single GPU if you can. Obviously not an option if you want more power than the fastest GPU available can provide but in all other cases you shouldn't use SLI / CF. There are a number of reasons:
1. It doesn't always work. If there's not SLI / CF profile for whatever game you want to play you just get the performance of one GPU.
2. Most profiles use AFR (alternate frame rendering). That means GPU 1 will render frame 1, halfway through GPU 2 will start rendering frame 2, once GPU 1 is finished with frame 1 it will start with frame 3, halfway through that GPU 2 finishes frame 2 and starts with frame 4 and so on. That means while you might see almost twice the fps the input lag stays the same. In fact it actually gets worse.
3. You need a motherboard that supports it and a PSU that can handle the power draw of two GPUs which adds to the cost.
4. With two GPUs next to each other they'll heat each other up and won't clock as high.
The end result is that you really won't get anywhere near twice the performance and it will cost you more than twice the money. A single GPU might actually get you better performance for less money.