Because of bitcoin's decentralized nature and its trading on online exchanges located in many countries, regulation of bitcoin has been difficult. However, the use of bitcoin can be criminalized, and shutting down exchanges and the peer-to-peer economy in a given country would constitute a de facto ban. The legal status of bitcoin varies substantially from country to country and is still undefined or changing in many of them. Regulations and bans that apply to bitcoin probably extend to similar cryptocurrency systems.
Your machine, right now, is actually working as part of a bitcoin mining collective that shares out the computational load. Your computer is not trying to solve the block, at least not immediately. It is chipping away at a cryptographic problem, using the input at the top of the screen and combining it with a nonce, then taking the hash to try to find a solution. Solving that problem is a lot easier than solving the block itself, but doing so gets the pool closer to finding a winning nonce for the block. And the pool pays its members in bitcoins for every one of these easier problems they solve.
The domain name "bitcoin.org" was registered on 18 August 2008. In November 2008, a link to a paper authored by Satoshi Nakamoto titled Bitcoin: A Peer-to-Peer Electronic Cash System was posted to a cryptography mailing list. Nakamoto implemented the bitcoin software as open source code and released it in January 2009. Nakamoto's identity remains unknown.