they do have the ability to produce fairly decent scans regardless the brand, and the type of the film as long as the film is a normal one
Exactly. Since there's considerable variability in C41 film that will still produce (more or less) normal scans, this is evidence of the adjustments that scanners make on the basis of the input image. The scanning software applies an algorithm to the actual image data, which performs curve adjustments on the separate color channels to produce a result that's expected (by the software engineers) to be fairly accurate.
The scanner can not apply exotic algorithms to produce an output.
I guess it depends on how you define exotic, but I'd call it that - non-linear adjustments with different average slopes for different color channels (=crossover). Here's an example of what my 4990 using the Epson Scan software does on a randomly picked set of (expired!) Portra 160 negatives:
This is with auto-exposure enabled so that the scanning software generates something that approximates natural colors. They're not really natural/accurate and would require manual adjustment, but this is also normal for all scanners that attempt to output color-correct scans from C41 film. The lack of an absolute benchmark or reference makes it impossible for scanning software to accurately reconstruct original scene colors based on just the image information.
Note how the curve adjustment above involves:
* Setting the black point
* Setting the white point
* Adjusting the curve slope for each channel
* Applying a non-linear shoulder compensation
* Applying a non-linear lower-midtone compensation
The exact kind of adjustments each scanner (scanning software) does, is specific to the scanner/software. So my Minolta tends to compensate in a totally different manner, outputting totally different (generally much worse) color corrected images.
The algorithms between a negative and a positive scan should be very different despite the same negative frame of film is scanned.
Yes, that's the whole point of that comparison

I'm sorry, it's slightly theory-heavy, so it requires some mental effort to understand what's going on. The purpose of that comparison is to establish the kind of correction curve a scanner (and scanning software) applies to color negative data to output a recognizable and more or less correct image. In the Epson example above we could avoid this whole routine because the Epson software conveniently already shows its actual correction curve, but most scanning software hides or obfuscates this information.
For slide film, there will be no algorithm, typically. Since slide film already contains the absolute reference for output colors on the slide itself, the only thing that matters is linearity of the recording device. This is a matter calibration of the scanner and its software. I suppose this is done by comparing the (inherently non-linear) A/D-converted output of the CCD array to a reference target and then working out R, G and B adjustment curves that are embedded into scanner firmware and applied to each signal being acquired. Long story short: there's no algorithm as such that needs to convert the color data from a color slide scan that the computer receives from the scanner. It's already 'good to go', and is (or should be) a linear representation of the original. We can do the same thing with color negative film and obtain this way a linear representation (more or less exact digital copy) of the negative: this is what the negative looks like with no adjustment at all.
If you scan the same color negative with the color negative settings, the scanning software inverts the signal and applies an algorithm to the input to reconstruct a credible color image. An example of such adjustments I've included above for my Epson scanner. If you then take the positive scan we just did above and open the Curves dialog in Photoshop (or GIMP or whatever), you can start making adjustments to the image on each of the color channels. Try to exactly (insofar as possible) mimic the output that the scanning software gave when scanning as a color negative. Once the images look (more or less) the same, you can tell by the curve shapes you've just worked out what the scanner is apparently doing 'under the hood'. In most cases, you will notice that the adjustments are non-linear. The scanner applies more magic than you seem to realize.
Repeating the same routine on different images can furthermore demonstrate that the adjustment is not constant - it's different for every image you feed through the scanner.
The conclusion from such observations is that whatever adjustments the scanner does, is really a set of assumptions based on no absolute reference at all - it's a wild guess of what good colors might look like based on a set of mathematical relationships applied to the image data.
Your experiences suggest that at least for your scanner, this often works out quite well. Kudos to the software engineers who made the scanning software you use. My experience is that the colors scanning software produce are often somewhat close to how they should be, but virtually never accurate. Statistically, it's virtually impossible that they're accurate much of the time, or even in a small percentages of the images.
Automatic color correction in a scanner with actual consistency/real-life reliability is theoretically impossible due to the real-world restrictions scanners have to work with. The only exception is if an ICC profile is available for a specific scanner and a specific film, and only perfectly developed film that has not deteriorated in any way (before or after processing) is fed through it, and only properly exposed scenes are contained on the film shot under nominal lighting conditions (which will be around 5000K or so). In all other instances, the only thing the scanning software can do is take a stab at it.
Are you talking about before the development or before? I believe the orange mask is there purely for the need of wet printing purposes.
After development.
No, the mask is not just there for wet printing. It's there to correct for the inherent shortcomings of the dyes themselves. This excellent website explains it:
http://www.brianpritchard.com/why_colour_negative_is_orange.htm
From this, you may pick up that the orange mask is not, as many people think, just a constant color across the entire film. Part of the mask is actually image-dependent and formed during processing. Since it's dye-dependent, the mask is unique to the particular film; it needs to exactly compensate for the shortcomings of these dyes, in this particular configuration of emulsion layers, etc. This is part of the reason why you see variation in the orange mask between film. Differences in processing also induce variation. The end result of this is that if you take two random bits of C41 film, especially from different manufacturers and/or from different eras, there will be quite distinct differences in how the color information is coded in the dye image and its correction mask. Scanners need to compensate for these virtually infinite possibilities. This is just one more argument why (1) a fixed benchmark is simply not present in color negative scanning and (2) ICC profiling is in practice rather limited in its applicability, because the number of profiles required would be quite ridiculous to cover let's say the scanning habits of an amateur who goes through the family negatives of the past 30 years. Your own use case of using expired film is another very significant complication.
I don't think film scanners have different unique translation of the pixels for each different colors of the mask.
No, so they need to mathematically wing it. See above. The consequence is that a scanner will automatically adjust each color negative image separately, and as a result, its output will vary wildly. That it looks natural to you, means two things:
1: The software of your scanner does a relatively good job at WAGging colors
2: You've simply never noticed the inconsistencies, possibly because you were just happy with the results and didn't see a need to dig deeper - which I think is a perfectly fine attitude and one that likely optimizes the pleasure of the whole process.
I do think that the story of your daughter illustrates not just how monitors vary (yes, they do), but also that people vary very significantly in how they perceive color and the degree of exactness with which they are able to discern and analyze hues. To a large part, this can be trained, although some differences remain between individuals. To me, it sounds like your daughter has a more color-critical eye than you and your wife.
No film scanner that I am aware of is provided with unique ICC profiles for each known type of film.
Indeed. And yes, there may be an ICC profile that comes with the scanner, but for color negative film, it will be nearly useless as it will necessarily be one particular kind of film (usually unspecified), processed and exposed under unknown conditions.
If you are talking about before processing I am sure you know it is washed off by the developer.
No color compensation mask washes off of color film. What washes out are sensitizing dyes and anti-halation dyes. These are unrelated to the compensating mask and the color reproduction story above.
In RA4 paper, the stuff that washes out is also not a dye compensating mask, but an anti-halation mask.