Is iPhone 5s unlocked and contract-free will be available on 9/20?

That depends on where you are. This is a world wide forum. Check the Apple website for your country.

Well you did not look hard enough:

http://store.apple.com/us/buy-iphone/iphone5s

If you are in the US, then all you need to do is click on the Store link and all the info that you will need re iPhone 5s is there for you to read.