Yes, you are missing the air box and filter.
Try marksmopeds.com, or mopedjunkyard.com.
If you run the bike without it for too long, you run the risk of it running "lean" and seizing up the engine. Maybe you could look at a diagram, and fashion some sort of an airbox to use.
Yes, the lever underneath the throttle is the decompressor cable.
Don't worry about it being broken. I'd concentrate on the airbox, and getting the bike to start first.
The decompressor by default is off, meaning that you'll have good compression. When you squeeze the lever it opens a small valve (near the spark plug) which basically kills the engine, damn quick.