go int system settings and select updates catogory
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Connect your xbox to the internet, sign in to your xbox live account. Launch the game and if your using an old version the game will automatically update. You will be prompted to confirm the update.
You can't undo it.
Microsoft maintains a list of titles that are forward compatible with the Xbox 360. If the title you are trying to play does need an update to play that update will be applied when you first launch the game assuming that your Xbox 360 is connected to the internet.
It should, although you will probably have to download and update for the game off of Xbox Live.
Currently, the Xbox 360 version of Minecraft is running 1.6.6 beta. This update came out before the adventure update of 1.8. It will take a while for the Xbox 360 version of Minecraft to catch up to the PC version of the game.