1) You may be thinking of the "Airy Disk" diameter which is a result of diffraction. That's a function of the aperture -- so it will be different depending on the f-stop you select.
While there are calculators that work out the Airy Disk diameter -- typically measured in micrometers (µm) -- that diameter has to be applied to the sensor based on the pixel pitch (which is also typically measured in µm).
In other words, the Airy Disk size created at a specific aperture to focal-length ratio is a fixed thing... but the number of pixels it covers depends on the sensor's pixel size.
Here's a site with one example of an Airy Disk calculator: https://www.cambridgeincolour.com/tutorials/diffraction-photography.htm
You'll notice two calculators on that page. The first one just calculates the size of the Airy Disk. The second calculates the size of the Circle of Confusion (CoC) but it does this by applying the size of the Airy Disk to the image size (e.g. print size). Adjust the print size (or monitor size, or whatever you use to display the image) and you'll notice the CoC changes.
2) This one is easier, but comes with some caution because there's a common bit of mis-understanding.
First, the easy, but not entirely correct answer... which is that you multiply the focal length by the camera's crop factor (which is 1.6x). E.g. a 100mm lens becomes a 160mm lens. That's easy... but also not quite honest (it leaves out some important detail).
If we pick on a lens -- say a lens with a focal length of 100mm -- the focal length of that lens DOES NOT CHANGE just because you attach it to a different camera body. In other words it's a 100mm lens on a full-frame camera and it's still a 100mm lens on an APS-C body. All calculations that involve focal lengths are based on that 100mm focal length for that lens. (I'm ignoring effects from focus breathing issues.)
What DOES change is the "angle of view" visible in the image produced by that lens.
The lens projects a (hopefully focused) image into the camera body. The lens is round. So the projection is a circle (it isn't "masked' into a rectangular shape). Much of the image does land on the area in the camera where the sensor is located. But much of the image spills off the sides of the sensor and just lens on other parts of the camera's innards.
On a "full frame" camera, the sensor measures 36mm wide by 24mm tall. The diagonal is just slightly more than 43mm across. So as long as the image circle that the lens projects into the camera body is at least 43mm across, it can fill the sensor.
On an APS-C crop-frame camera, the sensor dimensions are reduced by the "crop factor" and for Canon, that's 1.6. That means the width is 36mm ÷ 1.6 = 22.5mm wide. The height is 24mm ÷ 1.6 = 15mm tall. Hence your sensor is 22.5 x 15mm. (also the diameter is is 1.6x shorter as well... the number works everywhere).
The 100mm lens is still projecting that SAME image which has a diameter of at least 43mm across into the camera body... the sensor is still at the same distance from the lens. But now more of the image spills off the sides since the sensor is smaller.
It is "as if" you took a photo, printed it as a 4x6", then "enlarged" the middle 2.5" x 3.75" area out to the edges of the 4 x 6" frame (zooming in on it).
While this changed your angle of view, it does NOT change the physics of how a 100mm lens works. It's still a 100mm lens.
But photographers like to compose things in certain ways. If you take a "head & shoulders" framing of a portrait model... you have a narrower angle of view with the crop-frame body then you do with a full-frame body (using that same lens focal length). So you tend to back a away from your model in order to achieve the same composition. Since you backed away, you changed the focus distance. And since you changed the focus distance, you changed the depth of field. But it isn't the lens or camera body that changed the depth of field... it was the photographer's behavior (taking a few steps back to increase the focus distance) that changed things.
But since photographers want that composition (I just picked on the portrait as an example), you read generalizations that "full frame cameras" have shallower depth of field than "crop frame cameras" and produce better background blur.
Lastly, Canon only uses "true" focal lengths on these lenses. In other words an EF-S 55-250mm lens really does have a true focal length of 55-250mm (that's not adjusted for "35mm equivalent" just because the lens was meant for use on APS-C sensor bodies.)
3) It doesn't.
That was easy! diffraction limits (and the size of the Airy Disk for a focused lens) is based on the focal ratio (aperture to focal length ratio).
A 100mm lens has a focal length of 100mm because in a simple lens, if you measure the point at which the light beings to focus, it is designed to come to focus 100mm behind that point. (The focal length is measured from the objective lens element to the focal plane inside the camera ... the sensor.)
This would be true of a simple lens, but modern lenses with loads of lens elements complicate things. So if you pull out your ruler and measure it... you will often find the focal length isn't what you expect. So the focal length is actually based on what the focal length of the lens would need to be to produce that same angle of view if this were just a simple lens.
If we pick on the 100mm lens again... and pick on a Canon EOS DSLR (not a mirrorless body), then you need a total distance to be maintained. On a DSLR, there's a reflex mirror that needs to swing clear. That mirror is in the path when focusing, but it swings out of the path when exposing the shot. This means Canon needs to leave a bit of room.
On all Canon EOS DSLR bodies, they designed the body to position the sensor exactly 44mm inside the camera body interior (that's the measurement from the camera lens mounting flange on the front of the camera body to the sensor).
Imagine if you could put a Canon EOS EF 100mm lens (designed for use on full-frame bodies) DIRECTLY on the front of an EOS-M body (which doesn't have a mirror.)
The EOS-M (with EF-M lenses) uses an 18mm flange to focal-plane distance. The EF-M lenses are designed to focus an image 18mm behind the lens. The new EOS R (with RF lenses) uses a 20mm flange to focal-planet distnace.
If an EOS "EF" lens (designed to use a 44mm back-focus distance) is put directly on a body that only offers an 18mm distance, you wont be able to make the lens focus correctly.
So ...
The MAJOR function of that adapter... is to shim the lens out another 26mm (18 + 26 = 44mm). NOW the the lens is at the correct distance for it's focus to function correctly.
The secondary function of the adapter... is to supply the electronic pass-through so that the camera can still control the lens.
4) Yes - this would be the same for all EOS-M models.
I didn't go into the nuances of what an "Airy Disk" is (named for the english mathmetician and astronomer Sir George Airy who discovered the phenomena) is based on the wave-nature of light. You can do some Google searches to learn more about why they exist.
In any case, if you use any calculator to work out the Airy Disk diameter, you'll notice they ask for the focal ratio... but not the focal length.
Tim Campbell
5D III, 5D IV, 60Da
