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yes a g50 can run on minecraft
You do not need to own Minecraft to host servers for it.
From experiance I have yet to find a way that a chrome book without using an external programme can run minecraft.
If you are using window's, then use the Run program, and type in %appdata% and then run that, and it will bring you to a file containing the .minecraft folder.
Minecraft 1.6 is currently out. It does require that you download the new launcher to run.