No, you have to use your gamertag.
There is only one version of Minecraft for the Xbox 360.
No, the Xbox version of Minecraft is for Xbox360
The PC version of Minecraft can be downloaded from Mojang's official Minecraft page. The XBOX 360 version of Minecraft can be downloaded from XBox Live Arcade.
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.
Yes there is.
No, the xbox version is 1.5 patch.
You can't. This is because the version of the Minecraft Xbox 360 is different from the PC Version.
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 mod the XBox 360 version of Minecraft.
Yes it's a completely different system and your Minecraft on Xbox will be connected with your XBL account.
No. You can't mod the XBox 360 version.
No, but the Xbox 360 version is just an older version of Minecraft. You can reuse the old seeds that were on the PC, and they'll work on the Xbox.