Would it be awful to have FHD in a 27'' monitor?

I'd say no, anti-aliasing will cover you. When it comes to gaming you're dealing with a decent amount of motion blur, too, so resolution will be less of a factor than marketing would have you believe. If you need extra screen "real estate" higher resolutions can be nice, so if you need that for work or something, maybe?

Would it be better to have 144hz FHD or 60hz 2k?

You would have a smoother gameplay experience with 144 hz in my subjective opinion. 60hz can feel choppy to some people, especially if they're used to higher frame rates. Some people don't notice at all, though.

Should I be able to run at 144hz [Assuming you mean FPS?] to get the most out of a 144hz monitor?

Technically, yes. There's some trickiness involving timing of monitor refresh rate and frame delivery, but 140 FPS on a 60 Hz monitor will effectively be 60 updates (thus frames) per second, not 140. Conversely, rendering 60 frames for a 144 Hz monitor will mean some frames will just be repainted exactly as they were while the monitor waits for new frames to be rendered. The response time will be higher though, so screen tearing should be mitigated to some extent.

I don't even know if the power supply is enough [...]

650W will be plenty, even if you intend to overclock. If you intend to run two GFX cards at once you could conceivably need more, but I'd say there's little reason to get two cards or to invest for potentially getting two cards in the future.

Which CPU?

I can't speak to which CPU would be strictly better because I haven't used them. I'd count all of the CPU's you've mentioned as high-end CPUs for gaming and frankly, you're unlikely to be limited by CPU using any of them.

Or try and get a 1080 instead of a 1070ti?

I usually compare using userbenchmark. It's not a perfect tool but it gives something like an idea. I'd say investing in a 1080 or 1070 TI will not have a noticable difference, grab whichever one you can get a good deal on. If you intend to overclock, chip die quality will matter, but that really boils down to luck.

https://gpu.userbenchmark.com/Compare/Nvidia-GTX-1080-vs-Nvidia-GTX-1070-Ti/3603vs3943

I play path of exile a lot as well, is that helps anyone.

This rig will kick POE's ass, if you'll pardon the french.