Not to play. You can play singleplayer or multiplayer over xbox live no matter your setup. If you would like to connect another controller and play split-screen however, you must be connected via the hdmi cable, which unless you have an adapter to go from hdmi out to rgb/component in, you do need an HDTV with hdmi input.
Although you do not need an HDTV for an Xbox360 to work you will need an HDTV to be able to get the most resolution out of your Xbox
No
Yes you can, the demo just has a time limit.
the xbox 360 comes with all the cables you need
No, the Xbox version of Minecraft is for Xbox360
Yes. It's the only way you can get it. I believe you need to have Xbox Live to buy it, because you can not get Minecraft as a retail version, so yes I believe you do need Xbox Live to get Minecraft.
Xbox 360s come with the standard AV cable used to connect to a standard tube television. So, you do not need an HDTV. However, games do look a lot better in high-definition.
No.
no
To get Minecraft for free, you need to download it on Xbox.
Yes, you can play it on any tv.You may have to buy an adapter to hook up to an older tv but it's do able.
no.