You need an account, yes. When you start the minecraft program, it needs to log you in to your account.
You need a Premium account which you get when you register your Minecraft name and purchase the game.
No, you need to register and pay for the premium account online.
Anyone can register a free Minecraft account on the Minecraft website.
Minecraftnet is the only place where you can register the premium account that you need to play the full version of Minecraft.
It is unlikely, and also anyone can just register a Minecraft account themselves.
Not to register, just to buy the game and make the account premium.
Notch.
go to the minecraft website, click download and click register
Yes
After you register a premium account, you can download the client from the Minecraft website.
When you register an account on the Minecraft website, that's just a general account. You can play the free Minecraft Classic using it. To play the full game, you need to upgrade to a premium account by paying, that lets you play full Minecraft.