Non-alternative facts.

I guess that proves autoheal is the fastest way of building.

No, I don't.
Read it again.
Moving one pixel on the desktop does not mean it'll move one pixel ingame.

You still don't understand.
2.71286834 is the sensitivity where one count will cause a turn of one center pixel if and only if the DPI are set to 4336.738274819446.

The point is that this

is completely wrong.
No pixels will be skipped.
If the sensitivity is anything other than ~2.7 you will also be unable to move your view by one pixel at a time. For example at 2.1 ingame sensitivity each count will move your view by 7/9 center pixels. You are utterly unable to move your view by one pixel at a time.

No it's simply utterly irrelevant.
The 1 pixel limit is completely arbitrary. It doesn't matter if one count results in 1 pixel, 0.7 pixels, 2.3 pixels or 0.03 pixels of center movement. You don't have enough control or enough time to move the mouse in single counts because those would be <32µm steps. No one does that.
Literally the only thing you have to do is not go full retard and set your mouse to 1 DPI.
No one gives a shit if 800 DPI results in 1.5 pixels and 1600 DPI in 0.75 pixels. At the edges both will move more than one pixel anyway. Choose the setting which isn't broken on your mouse. If both are working flip a coin.

Do you mean x264? What's stopping you from using h264 hardware encoding? Do you not have a GPU?

To be honest this build doesn't make sense at all.
Why the 3 years old CPU? Did you really get it for free? Or did you already have that but for some reason no mobo?
Why the aftermarket cooler?
Why the GPU?

If you're going to pick one of the largest µATX cases it's not going to be very small.
If you want a case that's smaller than a µATX board would be you can't use µATX. Mini ITX is smaller.
Is this about minimal space overall or minimal space on your desk? You can just ditch the capture card and stream with a stupidly high bitrate (e.g. 50k) via NVENC/VCE/QuickSync to the encoding rig and reencode there. You could put it anywhere as long as there's power and a network connection.

#2903
Do you even need a new GPU?
Used 4770K/4790K might be an option.

i3-8350K wouldn't be that much of an upgrade. I mean a bit of IPC + clockrate if you actually overclock so overall maybe 20%? Considering that that upgrade would cost 350-400€ is it really worth it?

Until August we might get some more bullshit from Intel. Maybe the "8 cores but only on Z390 because fuck you" story turns out to be true.

#2904
Clockrate.
New mobo costs more. Way more.
Updating is free but not many mobos support updating the BIOS without a working CPU so if the retailer is unable or unwilling to do it you'd have to have AMD mail you a CPU (they'll do that for free), update the BIOS yourself and then send that CPU back (a pre-paid return shipping label is included).

Wrong.
TF2 does not use windows desktop pixels for the rotation counts (no game should).
Depending on the ingame sensitivity the minimum step that corresponds to the number of counts in one desktop pixel could be 1 ingame pixel or 13.245 ingame pixels or 0.0045212 ingame pixels.

Also if if corresponds to 1.1 ingame pixels then you will simply turn in 1.1 pixel increments, without skipping any pixels in between.
Pixel skipping doesn't exist.

Again, irrelevant.
Iirc the source engine uses float to represent angles. That means if we pretend that exponents and signs don't exist just the full precision of the 24 bit mantissa requires 16,677,216 counts per 360. At 12,000 DPI (and that's not really a thing, just multiplication and some fancy DSP footwork) that's ~1398.1 inches per 360. So about 116 and a half feet or about 35.5 meters for a full turn. And that's the lower bound, it's actually much higher.

See above. There is an actual answer and for the source engine it's utterly useless.

I won't check the actual numbers.
But setting the sensitivity via DPI? Come on.

So are you using 4336.738274819446 DPI now? If yes I'd like to know how you set that.
If not then it's not "pixel perfect". With 9050 DPI and 1.3 ingame sensitivity you'll instead turn by 0.47919759942756309392265193370166 center pixels per count (all other pixels are different). Literally unplayable.
Now imagine what would happen with 2.8 ingame sensitivity. 1.0321179064593666638334041648959 pixels per count. LITERALLY UNPLAYABLE.

The question is pointless and the answer is useless.

No mouse will allow non-integer DPI steps anyway, but if you can't set that then one count will translate to something like 1.0004 pixels of 0.9997 pixels, making the limit even more arbitrary and pointless.
It just has to opposite effect because non-native DPI steps fuck up everything.

Honestly I wouldn't bother with trying to get the best CPU for TF2 for this budget. +-10% barely makes a difference compared to the huge upgrade you'll get with any somewhat recent CPU.
Also if nothing has drastically changed 2 cores/4 threads get you 95% of the performance of 4c/4t (and beyond that you gain nothing). So a Pentium G4600 or older i3s would actually be faster than the R3 1200 and should be cheaper.

Look for a used pre-built (or just the CPU, RAM and mobo) and if the CPU isn't a Kaby Lake or newer Pentium or older i3 then upgrade that for 20-30 quid and you're done.
Or just used parts in general.
Keep one of the GPUs.

Why is it misleading?

It's obviously relevant for this.

No, your question is simply pointless.
The pixel directly in the center of the crosshair might move roughly one pixel per count at that sensitivity but all other pixels will not.
At any other sensitivity they will also not move "pixel perfect". At 25% slower sensitivity even that center pixel would move 0.8 pixels instead.
It's a completely arbitrary limit with no practical value.

Also it is related to the DPI of your mouse.

I think it's patented stabby math. 1080/400 = 2.7 but 2.7128 looks cooler. Or just random quoting.
Actual context from the article

It's about matching the degrees per pixel to the degrees per count and fairly pointless because like I said the game doesn't work in pixels anyway.

As usual stabby's explanation is bullshit.

Pixel skipping is not a thing. It doesn't exist.

Video games are not some static pictures made up of pixels that can only be moved by a whole pixel in any direction.
Anything you see is rendered from scratch. You're not turning in pixels, you're turning in degrees (or fractions thereof).
That's the resolution the game is working with.
So one count means the game will turn by e.g. 0.001°. That's the resolution you're limited by. At no point does the game go "Oh you want to turn by 0.03°? Nah mate, can't do that with this resolution." Only much later does the game even care about resolution.
Also anti-aliasing takes multiple samples per pixel to figure out where exactly a line is to mix the colours properly. I mean you know how it looks without anti-aliasing? That's because any pixel's colour is just determined by which colour its center is. With AA it'll blend the colour depending on how much of the pixel is covered by which colour. Obviously that means nothing needs to be moved pixel by pixel, any step in between is fine.

So the problem isn't DPI/CPI, it's sensitivity. Because that's applied to the counts. Usually it's just counts*sensitivity but maybe 1 scaled count translates to 10 ingame counts or 0.003°, that's completely arbitrary. But no matter what there's a specific number of counts for a full 360° turn. Let's say it's 1 billion. Now if you set your sensitivity to 2.5 billion a single count sent from the mouse would lead to two and a half turns. That's a problem. Don't turn up your sensitivity to >100 and everything should be fine.

tl;dr
Pixel skipping doesn't exist.
2.7128 is a sensitivity wo1fwood used for an example and not some magic value beyond which the source engine will stop working. http://www.teamliquid.net/forum/tech-support/333648-an-overview-of-mouse-technology

So your question is wrong. The game will register single counts and move accordingly. That means with 1000 dpi (and sensitivity 1 to not further complicate things) you'd have to be able to move your mouse in 25.4µm increments. Can you do that? Of course that's less than one pixel. But as mentioned above limiting it to "one pixel" which doesn't work anyway because the sphere->plane mapping means each pixel got a different width/height and pretending that everything will be fine below that and that the sky will fall above it is incredibly pointless.

2200G would be faster in games if you're willing to update the BIOS or get another mobo.
HDD see #2894
Get an SSD and/or faster RAM if you can afford it. (hint: you can)
https://pcpartpicker.com/list/Xqvv3b
Just an example. RAM depends on what's cheap when you buy it and mobo depends on how you want to handle the BIOS update (or rather whether you want to do it or not).

1. Yes.
2. Yes.

If you can get a B360/H370 mobo for a reasonable price then definitely yes.
You could get it to work on 100/200 series mobos with some BIOS modding because it's literally the same chip but I'm not sure if you want to do that.

Fuck the 212 Evo.
Get a better cooler.
There's quite a bit between 20£ budget cooler and 400£ custom loop. Maybe consider delidding. That'd help more than watercooling.
860 Evo?
HDD see #2894
1060 is overkill just for TF2.
650W is overkill.

So I'd spend less.
Maybe Ryzen 8 core instead if you're mostly streaming.

#2892
Seagate Barracuda or Toshiba P300 are faster and usually cheaper.
Maybe a better SSD.
Rest looks good.
Don't cheap out on the PSU.

#2893
It was just a suggestion. Especially the case is more or less random. Obviously if he doesn't need another HDD then he can skip that part. Maybe a 500GB SSD just because the budget allows it?