I think you may have misunderstood how Windows colour management works and its relationship to colour savvy applications such as Photoshop.
I guess, you just missed this feature in post-XP Windows. Most people think that it is the ez-"calibration" tool in windows, but actually the tool creates ICM, which is used for GPU-LUT calibration. You can use any XYZ(RGB) profile there, conversion tables will be loaded as board's LUT. This is universal and much better than loading with 3rd party LUT load tools, including those provided with calibrators. So the graphics software just need to support basic sRGB, and no ICM is necessary (when OS "working" space is set to sRGB).
In Windows XP it was different - OS was providing only means of conversion (profile management) to ICM-aware programs, and no hardware calibration.
The monitor profile will not be sRGB so the sRGB profile in your Windows system should not be used. You will need to use a calibrator such as X Rite or Datacolor Spyder to calibrate and profile your monitor.
No. Not exactly. Of course, color calibrator (colorimeter) is a preferred solution, but also an expensive one, and not always perfect (on some monitors). I would say, it is perfect only for monitors with "uploadable" 10bit LUT. BTW, some cheap LG monitors had calibrator attached 7 years ago, didn' see them for long...
The software I am talking about (seems you are unaware) uses "fishnet" pattern test for balancing RGB to (visually) optimal grey. It is done in the whole range of brightness by specific GAMMA-RAMP formula. Either 1.8-2.2 or sRGB, by your choice.
Now, consider the monitor hardware (the LCD preamplifier factory configuration) - it is usually limited around sRGB, or AdobeRGB gamut. Inside the gamut there are nonlinear distortions, which we correct in software (GPU-LUT). That depends on monitor setup, so I recommend switching on the "sRGB" option if it is available.
So when it is in sRGB limits, and the gamma distortion was corrected, we can speak about more or less sSRB profiled monitor.
That is not for HDR monitors, where limitations are moved out, and we do not know how much without a colorimetric profile. Well.. with such gamma-correction it is still better that without.
This does not work on some monitors with exotic subpixel configuration, can probably fail on OLEds, where subpixels are not even.
You cannot use a camera to calibrate and produce an ICC monitor profile - at least as far as I know
I am a scientist. At least I was before becoming a sensors engineer.
I am always asking, WHY can't we do it, and how can we overcome it?
Leaving it just because one have no idea, or someone said it is useless is not an option.
Now talking about approach and problems.
1.Initial approach. I think about Argyll manual for RGB printer.
2. I need to make a brightness independent profile. I guess, "absolute colorimetrics" is not acceptable. Then, what intention should I use?
Maybe just tweak the brightness span (from deeper than black - to - brighter than bright) in photoshop linearly. Then use relative colorimetric intent in Argyll.
3. Lighting. Flash? Daylight? Probably white LEDs from left and right (a pair, or four $5 keyholder lights?). Because the monitor is LED.
... Or maybe shooting in the dark under the light of the monitor itself?
4. harder part with the camera. I have a Rebel(100D) which does not provide RAW output... and I am lazy installing Magic Lantern (probably I should). Can we do it with JPEG from the camera? What are the settings? Manual ISO. Manual white point. Fixed exposition. What else?
5. White point? Did not use it for long, but seems there was a manual whitepoint option ("point it at the ceiling" feature). Should I point it at the a)IT8 target white patch (probably no). b)ceiling, c)at the photo-paper surface, d)at the monitor screen (white image), e)at the light source? I guess it should be "d".
I have to try it the next week, when I find an evening or two for experiments. Before that it would be great hearing your suggestions.
BTW. I kind of "profiled" scanner without having real IT8 target. I used old iPhone's IPS screen, which is a high grade sRGB device (now they make wide gamut, like Samsung, but specifications are obscure). I uploaded there IT8's TIFF image, and put it on maximal brightness.
Scanning was hard, needed tweaking in Photoshop. The result was so-so... But much better then no profile.