How do I show a "model" in a movie just like it is actually in the movie? I go this set up to show, I put A Movie in, then went to nodes, added the movie, scale set to render size, and rendered layer is connected to  Alpha over connected to composite .. the model is barely showing up .... I had to add emission to the material to the model to get it to do that, but it is not even very realistic looking.
I did not have your movie, so I substituted a brick image. I was able to achieve this result:



As you can see, it is not transparent at all, and nor is the brick background weird. I used this RenderLayer node setup:



Note the values in the Alpha Over node, which I changed to 0 and 1. The 0.527 for the Fac: value would have made your model transparent. The Premul: value could have led to the background distortions. Also note that I checked Transparent in the Properties panel > Render tab > Film dropdown. The modified Film dropdown should look like this:



Here is a modified .blend file. You will have to substitute your video back in to the RenderLayer node setup, though.