- Do I download the games to hard drive?
- How much is the service?
- Does Steam OS make the experience better or what?
Yes, games are downloaded to your hard drive before you can play them. You can select the location where the games are to be downloaded and stored by specifying a custom game library path.
Steam by itself is free to sign-up and use, however most games, to the exception of free-to-play ones, are paid and requires you to buy them. You can pay trough multiple means, including Credit Card and PayPal. You can also set up a Steam Wallet account to store funds dedicated to Steam purchases.
Steam OS is still a bit of an experiment for the upcoming Steam Boxes, and for dedicated Steam gaming computers. It doesn't make the experience particularly better as it is more of a Debian Linux distribution with Steam starting in Big Picture mode upon startup -- this implies the games you want to play must be running on Linux (indicated by the OS icons above the "Play" / "Buy" button on the game's Steam page), however their number is increasing and many are already available. For some games (mostly Source engine-based), there can even be a performance increase as they are optimized for the platform (more specifically, using OpenGL) and as there is minimal desktop interface overhead compared to Windows.