I don't see any places on the drawing where you need a stripe of light; only patches. Therefore, LED strips are a bit silly. Just wire up some banks of LEDs. It really isn't difficult.
If you do need to mask light, on things like EL wire, plastic fiber-optics, etc. Don't use duct tape, just paint the surface either with black acrylic paint or black plasti-dip.
It's sorta up to personal preference whether you make film translucent green (either via green-tinted film or translucent paint) and using white LEDs, or to leave the film clear and use green LEDs. Each provides a different effect, it just depends on what you're going for.
Yes, those are examples of what you're looking for. The thickness of the film mostly relates to flexibility and durability. If you decide to glue a layer of plexiglass on top, then just use the thin stuff. If you want the film to serve as the top surface, then you'll want something in the at least somewhat thicker range. You might need to talk to a supplier or see if you can get samples to figure out just what thickness is right for your needs.
The film is plastic, though I'm not sure what specific type.