These light or frequency shifts are relative to the “speed” of light, so it does in fact prove that the speed of light changed, otherwise all light would be the same color because it’s speed- “frequency”- would be the same. We wouldn’t be able to tell which galaxies are further away than others.
No, no and no. You deseperately need to take Physics 101. We can easily explain and predict red shifts w/o needing the speed of light to change. The speed of light is a constant -- it is exactly the same regardless of how fast you or the object emitting are traveling.
The speed of light is a constant, the distance it has to travel is what causes the shift in color, not whether it is speeding up or slowing down.
Here's a little experiment for you to try.
Have a friend stand at the end of the block while you are on the other end.
Have them say in a clear normal voice "I am Standing here" repeatedly.
Start walking towards them. As you get closer you begin to kind of hear them, but not distinctly until you are much closer.
This is an example of the Red shift in the Doppler spectrum indicating closer distance the light has to travel.
Now, start walking away from them until you cannot hear what they are saying.
This is an example of the blue shift in the Doppler changes. The volume has not changed, but the distance it has to travel has.