What parts are publicly visible?

The only publically visible part is the title of your website and a website picture (if you have set one). Here is an example of my family: The Gatewood Family Website

Why is this public? The public page is used to get all of your members into your website and that's it. The content inside the website requires a member account to access. Once you have everyone in the site, I recommend turning off the public profile page.

Who can access the data? Only those you have granted access to your website will be able to view the content in your site.

What can search engines see? The engines will only be able to see the website name and group picture.