First, let's discuss why you see a white dot when you point an IR remote at your camera
The key to understanding why anything recorded by an RGB sensor is white in an RGB representation of the recorded image is to understand that if exposure is high enough ANY color of light, visible or otherwise, will cause full well capacity for red, green, and blue filtered pixels. This is because each pixel well does not really record any color - it just records a brightness value. The filters mean light that is not the same color as the filter will be negatively attenuated and much less of such 'off wavelength' light will be allowed to pass through the filter. But as pretty much any spectral response curve for consumer cameras will show, a little bit of all the wavelengths of visible and non-visible (to humans) light can make it through each color filter and will affect the resulting image if the light in the recorded scene is bright enough at that wavelength.
In the spectral response curve above, we can see that response to light above 800nm is relatively uniform for this particular sensor. This is fairly representative of most sensors used in consumer cameras. Any light at wavelengths above 800nm striking the sensor would have an equal response in sensels filtered for red, green, and blue respectively. When those luminance values are interpreted by the algorithms that create color values for each pixel location, those equal values for R, G, and B will be interpreted as white. This is why most cameras have infrared cutoff filters in front of the sensor - so that IR light doesn't fool the camera into thinking everything is more white or more a shade of grey with equal amounts of red, green, and blue than we perceive it.
At the other end of the spectrum, UV light is light that has a shorter wavelength than humans can perceive. Most cameras used for artistic photography (as opposed to scientific or industrial uses) also have an ultraviolet filter in front of the image sensor. But like most photographic filters, if a light source is bright enough some of the light filtered for a particular wavelength will still get through.
This is what you are seeing in that white dot.
Enough of the IR (or more likely near-IR) light emitted by the remote is making it through the filter stacks and Bayer mask in front of your sensor to cause an equal brightness value to be recorded by the respective red, green, and blue filtered sensels at the area on your sensor where that light is falling.
Now let's discuss printing IR light recorded by a camera's sensor
If the camera, such as your camera in the question, has recorded the IR light but misinterpreted it as visible light then the result of printing that image will be colors in the visible spectrum.
If, on the other hand, you use a very specialized camera that is able to discriminate IR light from visible light there are several things that could happen. Two of the likely possibilities:
- Your imaging system could convert the IR light to 'false color' visible light colors and send instructions to the printer to print the image using those 'false' colors within the visible spectrum. You would be able to see the 'false color' image in the visible spectrum. This is what many night vision and thermal imaging systems do. They convert IR light to the visible spectrum, either as a monochrome image or as an image where various wavelengths and/or intensities within the IR spectrum are translated to various colors in the visible spectrum.
- Your imaging system could maintain the correct color of the IR light and record it using a color space that allows it to be identified as a particular wavelength of IR light. To print from such a system, you would need a printer with inks that are capable of absorbing all other wavelengths of light except IR, which the ink would reflect.
If you viewed such a printed image from the second scenario above under full spectrum light you would either see black if the ink fully covered the surface of the paper or gray if some of the visible light reflected by the white paper is allowed to be reflected through the gaps between the ink droplets.
Finally, let's talk about printing UV
UV light that insects can see but that humans can't would be pretty much the same thing as IR light, just at the other end of the visible spectrum. You would need a camera that can discriminate UV light from visible light and record it in a color space that preserves that capability to discriminate the various wavelengths of UV from visible light. You would then need a printer with inks capable of reflecting UV light while absorbing visible light. For the insect to see the UV components of the printed image the print would need to be illuminated with light that included those UV wavelengths that the inks used to print the image would reflect. If only visible (to humans) light was used to illuminate the print, there would be no UV light to be reflected by the UV inks and the insect would not see the UV components of the light from the scene.