Sony Connect is the old name for eBook Library. And the name of the Sony eBook store is called The eBookStore at Sony.
Adobe Digital Editions is what you use to register your 505 so it can view ePub and PDF with DRM. In order to be able to share eBooks, you'll need to use your sister's registration info in order to be allowed to view her eBooks. Then after that, anyone in DRM laden ePub or PDF that you purchase you'll be able to share.
To find out more about Adobe Digital Editions, just go to
http://www.adobe.com to find out more.