Regarding the light gathering you mentioned at 5.6, can you confirm or correct me if I've got this right or not. At 5.6 on aps-c, the amount of light hitting the sensor is about the same as the amount of light hitting the sensor at f8 on a full frame because the sensor is larger. And so there's the same amount of light and DOF on aps-c at 5.6 as f8 on FF?
This is complicated. The aperture and focal length of a lens are properties of the lens, and do not change simply because the sensor is smaller. An f2.0 lens is an f2.0 lens regardless if it's on a full frame camera or APS-C camera or any other sensor. This means exposure settings will be the same regardless.
On a 1.5x crop APS-C sensor a f2.0 50mm lens will have the field of view and depth of field that a 75mm lens would have on a full frame sensor. But it's still an f2.0 lens, and if correct exposure requires ISO 100 and 1/500th of a second shutter speed, it'll need ISO 100 and 1/500th on an APS-C camera. You don't need to raise ISO on the APS-C camera; doing so will overexpose the image.
This is because the amount of light hitting the sensor per unit of area is the same. For example, if a bucket gathers 10 raindrops/second/square foot, an Olympic sized swimming pool also gathers 10 raindrops/second/square foot.
As for how much total light the sensor is actually gathering, yes, the full frame sensor gathers more light than an APS-C sensor. Again though, this does not change exposure settings. Because a smaller sensor gathers less light overall, the signal-to-noise ratio is less favorable. Thus a smaller sensor will have more grain/noise than a larger sensor, assuming equal technology.
If you take a pic with a FF and APS-C camera and use identical settings, the full frame camera will have less noise. If you're trying to match noise levels, that means you'll have to lower the ISO on the APS-C camera by about 1-1.5 stops. It's tricky making these comparisons though because sensor tech varies between cameras, in-camera noise reduction varies (both automatically and by user settings), etc. The amount of digital gain that ISO settings provide should be relatively universal because it's part of the "exposure triangle", but the amount of noise this creates in your image will vary by camera.
For example, many users of the Canon R5 noticed that when they switched to the R5 Mk II that there was more noise in their images. Not because it exposed differently, or because the sensor was smaller (it's exactly the same size), but because the sensor was different (stacked instead of unstacked) and produced more noise at the same ISO settings. But the R5 Mk II will definitely produce less noise than an EOS 1D from 2002.
Thus, direct mathematical corollaries aren't always going to be exact; a 1.5x crop doesn't necessarily mean you'll have 1.5x the noise, or need to drop ISO 1.5x and slow your shutter speed by 1.5x to match the noise of a FF camera. It's not a bad rough guess though.
Does this explain things, or did I just confuse you more?
