I don't think you can, you'd still need to buy it from ICANN. Now if you buy paid hosting a lot of times they'll give you a free domain as part of the deal.
Chat is basically talking to someone. You could do online chat, etc, going on quick chat on windows messenger or facebook etc. Think about it, its in the name ;] Yasmin bums homeless people :]Youu...
You can only use the web browser to play the free updated version. Under the "Buy Now" button there is an "In Browser" and "Download" option. I don't think it saves anything though and you won't be...
There are programs you can buy for the computer that allow you to do that. Or you can go to a local media store and find equipment that will allow you to do so.