Dust (and scratches?) can be detected with an infrared scan. The IR scan is only used to detect defects, and then something like a spot removal tool is automatically applied to the defect areas.
Technically, yes. I know a few people have done it. In a practical sense it is very difficult and you are unlikely to get it working without a lot of trial and error. The tricky part is that the IR image needs to be perfectly aligned with the rest of the image data, which introduces a number of difficulties.
• You can modify a sensor for IR, though this is often a costly and difficult modification. But even if you do so, the IR focal distance is different from the visible light focal distance. So for every shot you need to refocus for IR, but also ensure that the refocussed IR image is exactly the same size as the visible image.
• You can use another sensor that is sensitive to IR, but its probably not going to have the same resolution, you're going to struggle to somehow have both cameras see the target image, and then once you get both exposures, alignment becomes a problem.
https://www.hamrick.com/blog/digital-ice.html