You cannot have dark without light.
Not true in the case of dark matter (for the general case, see below). Dark matter is called "dark" because it appears that it doesn't absorb or emit electromagnetic radiation - light! It can interact with light via gravitational lensing, but dark matter particles have no electromagnetic charge (we think) and so are considered "dark".
The only thing faster than light is dark (i.e. shadows)
This is true, as the video explains.
Does this make "dark matter" mere shadows of extremely bright objects?
This is the meat of the question, and the answer is a clear "no". First, any "bright objects", while capable of casting a shadow of something else, will emit electromagnetic radiation.
Okay, so why can't there just be non-extremely luminous objects casting a shadow? One reason is that the dark matter simply isn't where these shadows should be. Many galaxies have a dark matter halo that extends far beyond the galactic plane. Any light sources emitting light (that is then shadowed) would have to be on the opposite side of the galactic disk. This is simply not the case.
The second, more convincing, reason is that dark matter has mass. In fact, that's the reason the idea was first conceived (to account for anomalies in galactic rotation curves)! Shadows don't have mass; therefore, dark matter cannot be explained by shadows.
Is that also why it has to get dark before we can really see the majority of stars (subjective experience)?
No. I don't know for sure, but I believe that that's because the Sun's light is still blocking out the light of distant stars.
Addendum after edit to question
Can you provide sources for your claims?
I think that they're pretty well sourced! The first section can easily be checked via Wikipedia (which I assumed you had seen). The rest seems to be well-sourced, too (aside from the last bit, which is, admittedly, unsourced but only tangential).
Also I didn't say you can't have DARK MATTER without Light , I said you can't have Dark, as in Darkness. I think you're getting hung up on Dark Matter which is a big part of my question, but not the entire question.
Okay, I may have misinterpreted this.
Darkness is, by definition, the absence of light (electromagnetic radiation). So no, you don't have to have light for there to be darkness.
Also, are you claiming that all darkness in space is dark matter? I don't like to assume but for scientific purposes (not an accredited scientist) would we not agree that the measures made on dark matter were on a sample, and not the entire universe?
I never said that, but you did. Your original question asked if dark matter could be shadows. The answer is no.
So to further question this, do shadows not exist in space?
They exist. Any object blocking a light source casts a shadow:
This happens to have been used in the video, so it shouldn't be new to you.