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I assume you need to have the Android stuff (AVD, eclipse plugin, library files) for the Android portion to work. I would start here: http://developer.android.com/sdk/index.html

Yeah, the idea is that you can develop and test your program on desktop and then deploy it to Android very easily. You can ignore all the Android stuff and just deploy it to desktop if you want...

On a personal note I highly recommend libGDX. I've never used JMonkeyEngine, but I've seen some pretty amazing things done in it. You'll have to try both to see which one you like better.

For more info on opengl, I suggest you start here.

I also suggest you look into the game development libraries available to you, which wrap opengl in an easier-to-user Java interface. Check out...