Bitcoin is a digital currency that is rapidly gaining popularity because it solves many of the problems of other forms of currency. It's created and held electronically and can be used to buy goods and services or transfer money anywhere in the world. Bitcoin is the first currency to be globally accepted and there is no currency exchange, no minimums, no limits and it does not require a bank account.
The fee goes to the miner who mines the block that includes your transaction.
You can buy bitcoins from either exchanges, or directly from other people via marketplaces.
Nobody owns the Bitcoin network much like no one owns the technology behind email. Bitcoin is controlled by all Bitcoin users around the world.