These are very important questions.

In what ways is Keychain safer than simply saving private keys in our browser the normal way?

While saving keys in the browser isn't really an issue, putting them into websites is. When you put a key into a website (or any data really) you're giving it to them and you have to trust that they don't misuse that data, either on purpose or accidentally, AND that the site doesn't get hacked. Many people have said that it doesn't matter if steemit.com gets hacked since the keys are only used on the client side, but that's not true. A hacker could modify the website code to steal the keys entered on the client side.

If you use keychain, then steemit.com or any other site never gets access to your keys. Instead they just request that the extension sign transactions with your keys on their behalf. This means that even if a site gets hacked or does something malicious they can never get your keys.

Who will potentially have access to our data saved within Keychain?

The code for keychain is open source and is available to anyone here: https://github.com/MattyIce/steem-keychain For the maximum security you can download the code straight from the repo and install it in your browser that way rather than through the chrome or firefox web stores. This ensures that even should the chrome web store account that publishes the extension get hacked and a malicious update be published, your keys would still be safe.