Depth of field and crop factor misconceptions (FF and MFT equivalence)

“Biscuits Alive” posted that video where he explains in detail how the FF and MFT equivalence works. He writes:

There is still a lot of incorrect information out there about –
-Depth of field
-Crop sensor vs full frame cameras
-Speedboosters
-Light refraction

And it seems many people who profess to know all about their camera gear, don’t actually fully know some of the basics regarding-
-Aperture
-Focal length
-The focus plane
-Crop factor
-The Circle of confusion
-ISO
-Image noise

So I decided to talk about all of the above, and I drew some simple illustrations for you, and also took a few photos to help show what is actually happening to the light as it travels through our cameras lens.