No, it only costs if you wish to upgrade to the premium version.
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It is free to make an account on the Minecraft website, but you have to pay to play the game.
You have to make a account and Buy the game it cost $26.95.
It does not require money. You can either make an account to make a playlist or download (w/o account)
It does not cost anything to get a minecraft server. You simply download the Minecraft_server.exe from the minecraft website download page. Then, you run it to make your own server.
Registering on minecraft.net is free, but it costs $30 USD if you want to buy it.