1) There is no company behind it. Noone is in control. Also you could say every user is in control. Bitcoin brings to the table the invention of the decentralized asset ledger, also known as the Blockchain. It allows everyone to not depend on any third party in order to pay to another person, and more (remittances with negligible fees, micropayments, appliances paying for they own needs), and not just money applications (digital assets, smart properties, stocks).
In a way, Bitcoin is doing to money like internet did for communication. For example, now you can create a website and you don't need to ask for licenses or permission to anyone and it's available to the world to see. With bitcoin you can create a financial application and you don't have to ask any banking authority for permission, you see the need, you make the app and people can use it if they want. It is open for innovation. Also bitcoin would be the equivalent to the TCP-IP protocol in the internet (transmission of packets of information), over which another protocols and applications can be run.
There are companies that give services based on bitcoin, like money exchangers for example, but bitcoin doesn't depend on them, they can thrive like coinbase or they can fail like mtgox and the world keeps turning, since the fundamentals of the technology are the same, and if that's of some value for the people around the world then bicoin will keep having value.
Here is a video that summarizes the technology if you are onto it:
2) The market value is a continuous discovery process involving everyone that uses it. There is a lot of psychology in there. It's a mix of real utility, perceived utility, expectations, greed, speculation, normal buying and selling, etc. The thing is, since the money production is determined and previsible since the beginning, (can't be artificially manipulated) it's theorized that the monetary value of the bicoin network must increase to accomodate the wealth that is deposited into it, and not be so volatile when it's used for big transactions. So all the users are affecting the value at the same time. It's fun to watch, and scary at the same time, like a rollercoaster. The general perceived consensus is that as years pass and more people use it, the volatility will keep decreasing and will become more stable.
3) The main risks for me are that a fundamental flaw is found in the
underlying technology which couldn't be fixed, or that people decide that the technology is not worth, looses interest, stop using it and becomes irrelevant.
The biggest risk for individuals i guess that they loose their money for being careless, not understanding the basics on operating securely (e.g. using unencripted wallets on windows), or that they buy more bitcoins that they can afford to loose, for especulation, and since the price is still very volatile they can loose what they don't have. Or that . You see, this is still in a phase similar as internet in the pre-1994 years. It's still mainly for pioneers, believers, and risk takers. Like any new technology it needs some time to be ready for the masses and to become stable and easy enough for our moms to use.
4) It's basically a distributed ledger, so the annotations and operations will be resumed when the backbone comes back up, I guess. I'm really more worrried of a solar storm happening again like the one that happened 155 years ago, frying all our electrical devices.
EDIT: words