I currently don't know of any free host that also provides free domain names. What you'll need to do is get them separate and then tie your domain to your hosting account.
No it tricks you by the name it got me a virus when i was playing in the middle of it so i hadn't played then. remember do NOT PLAY
Your best bet for a 100% free domain that you have control over the DNS is either win it in a contest somewhere
I don't know of any site that offers both a free domain and free hosting to be honest, you'll probably need separate sources for them both.
Yes! There are many methods out there on the web.