I don't use a green screen so take these suggestions with a grain of salt.
1. You do want something matte. I'm not sure what material would be best but anything shiny reflects light, causing the areas that are hit most with light to reflect the color of that light source and not the green of the material. Matte absorbs light, therefore you get a background color with less highlights on it.
2. Green and chroma blue are the most popular I've seen. They are colors that don't clash with human flesh and can be easily removed in lightroom without altering skin tones. Sometimes a neutral grey may work too which has the benefit of easy white balance.
3. Not sure, photoshop is plenty good enough.
4. Well, this is all a matter of ease. Ideally, you'd want to control your light on the model and on the background as well, so using 2 side fixtures would give you the most control and the best results. What's the point in doing all of this if you didn't want to get it as close to perfect as possible? I remove cosplayers from backgrounds all the time without using any equipment, but it means I have to spend a lot more time in post. Personally, if you're taking the time to make and carry around a green screen, then it's worth carrying the additional lighting to make it work.