1. On the right side there's a sidebar, which lists recent docs of the user's company.
2. Click on a doc in the sidebar would open another UI: doc card. A doc card shows the content of a doc.
So the answer your questions:
(a) mentioned above
(b) the iframe doesn't need anything from the page. Users may copy content from their Slab doc to the page. An example use case is the user go to Google Docs to write, and they need some content in Slab, so they open the Slab extension, find their docs, and open it on the page so that they can refer/copy content.