2. If you want to register the (left side only) trademark with the US government, go to the site mentioned above. (Fees are only $335 though). You can register your mark in US states and other countries as well.
3. In order to register a mark, you must actually be using the name in some way. You can't just buy a domain name, mark it, and never develop the website or related business.
Hope this helps.
(Put "tm" on your name now)