It would take a very long magazine article or a large chapter in a book to answer all of those questions -- a posted reply in a forum would be inadequate. One question alone in your list could take several replies!
Since these are basic questions, you should first do some searching on your own and then come back with a few more specific questions when you find something you read confusing.
As for YouTube links to demos using diffusion gels for lighting, we could do some searching under various terms to find some links, but you could do the same searches on your own.
Your post comes off as someone who has a classroom assignment to write and wants help in writing it.
Some of this is common sense, like what do you think happens when you take the soft light that comes from a bounce and then diffuse it further by passing it through a diffusion material? It generally gets softer -- though you are always limited by the size of the soft source. In other words, if you completely fill a bounce surface evenly from corner to corner with no variation in brightness across the surface, then the light can't get any softer until to becomes a larger surface, in other words, if the size of the bounce area is 12'x12' and you pass it through a 12'x12' diffusion frame, it can't get any softer if it was already a perfect soft even 12'x12' bounce. In reality though, no bounce is perfect so passing it through a second 12'x12' diffusion frame would make it easier to fill the 12'x12' area more completely and evenly, but ultimately it is the 12'x12' size relative to the subject that determines it's softness.
"Diffused light" is a type of soft light, though broadly speaking, all soft light is soft because it has been "diffused" in some manner. There are many degrees of softness to a light, from barely soft to super soft. Now you can soften a light by passing it through a diffusing material or by bouncing it off of a material, or both, and the type of light itself may be a soft source too.
Just keep in mind that the general rule is that the size of the source -- and in this case when you hit a diffusion frame or bounce card with a hard light, then the diffusion frame or the bounce card is considered the source -- relative to the subject determines the sharpness or softness of the light on the subject. "Relative" is key because you can make a 12'x12' soft light and move it farther away so that from the point of view of the subject, it is the same size in their vision as a closer 4'x4' soft light, and both lights would create shadows of the same softness, the only difference is the degree of fall-off in intensity over distance, not the degree of softness. But all of this assumes a "perfect" diffusion surface, that light is evenly filling the diffusing surface from corner to corner, when in reality, you often have a hot spot with fall-off around the corners.
A good example would be when you shine a light through a 12'x12' frame of thin diffusion compared to heavy diffusion, with the thin diffusion the light would create a hot spot in the middle which is really the size of the soft light, not the 12'x12 area. And some diffusion material allows some hard specular light to leak through the weave of the material, creating a soft light with a faint hard light mixed into it.
You see, I wrote all of that and I only was setting the stage to discuss soft light. It would take a book to answer all of your questions.