No you don't. Its just a 1-off $4.99/£4.99 payment.
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Minecraft is a onetime Purchase not every game is a pay to play...pay to play meaning you pay per month to play.
No, you only pay for it one time. All updates are free.
Minecraft is a one time fee for $26.99 USD
It is a downloadable game only, just like the PC edition, so you must have internet on your Xbox to go onto the marketplace. The game itself is a costly 1600 Microsoft Points, or $20, but it's worth it, and is constantly being updated every month or so. A demo for the game is available in the marketplace as well, and if you haven't played any edition of Minecraft before, you may want to try the demo. However, he game's demo only includes the tutorial level, which is in the full game as well, but you cannot save the tutorial, and you may also not create your own worlds and save them.
No, there is only a one time fee to buy the game now at minecraft.net. I think it is 25 bucks now. but the good thing is that once you make a Mojang account (the company that sponsers Minecraft), you can get minecraft on any other computer free of charge. But to answer your question, there is no monthly charge to play the regular game.