I love this question. Congratulations, either you are a philosopher or a really technical guy!
An image file contains data points (DPs) with rgb values.
In graphics arts and resolution "DP" Stands for "Dots per". A "dot" is the minimum element of a printed image. The difference is that on a printed image you either have a dot or you do not have it.
On an image file, the minimum element of an image is actually a pixel, but it is a variable one, it can hold different values of information, it is variable information with some two-dimensional coordinates. So I would change the DPs for simply pixel. (In more mathematical terms it is a matrix of values, not data points).
(I would not use also the term "point" because a point "in space" has no dimensions but a dot and a pixel (potentially) do or can be defined. In some other disciplines, for example in a 3D object it can be made of a "cloud of points" which individually have no dimensions, but can be used to generate an image)
Those values switch on/off computers' pixels.
Yes and No. Unless you only have a 1-bit system (old LCD display panels) the computer can display variable values, not only on-off.
But here is my contribution to the graphics arts :o) I have, for some time now, using a neologism for the pixels on a monitor. I call them Dixels (display units) These small elements in charge to display an image on a modern computer are an intrinsic part of the hardware. It is there either the monitor is turned off, or even if it is broken in parts. It has a fixed size. It is not a part of an image, but an element meant to display them.
On the one hand there is the image file, composed of DPs; on the other hand there is the computer screen, as a grid of boxes or pixels.
On one hand, we have the image file with an array of values (matrix). On the other hand we have a computer screen as a grid of dixels. :o)
If each DP is put on each box or pixel of the grid, then the image has its 'natural size' on a particular screen.
Yes. When a pixel is displayed at its natural 100% dimension it matches the natural size of the computer's dixels.
When an image is cropped, the number of DPs is reduced and so its size (correct if wrong please).
When an image is cropped you take digital scissors and remove some rows or columns of this matrix of data.
Resize an image Open it up on a different screen. (these two issues are logically the same, I believe.) If the image size is increased using some software, then I guess each DP now occupies more than one box?
There are two similar concepts, Resampling, and Scaling.
Resampling is making a new matrix, a new image where you can, for example, average the values of some adjacent pixels according to a given proportion. If you have one checkboard of white and black pixels and resample it with some specific algorithm, you can have a smaller matrix with a bunch of gray values.
But when Scaling the matrix (image) stays intact, the only thing that has being averaged is the display.
One dixel has now several sets of information. "Display this pixel, and a part of this other pixel, and a bit of this other one" then the dixel simply "averages" the values.
But how is an image on its natural size shrunk down being that there are no boxes left? Are some data points automatically removed of the image file?
With the two concepts described above, you probably can answer this. Yes, you can potentially mess up the photo of your cat resampling it down to an image of 1 pixel. You can no longer recognize your pet.
You can not resample an image to 0 pixels, because technically you do not have an image to save anymore. You probably can edit a file and remove all data from it... and save it but that is hacking a file, not resampling it.
But with scaling the photo the information is still there, you probably can not recognize the cat scaling it down, but you can simply scale it up let's say with the scroll of the mouse.
An addendum to my dixel concept. There is one that is actually being used in image capture devices. The sensor of a camera does not have pixels, it has sensels. https://en.wiktionary.org/wiki/sensel