Let users build a list of their favorite posts/pages from the site and share their list on Facebook, via E-Mail, or download content as a Web-app for
Yes, using HTML5 Storage, every user can create his post list and keep it stored in his browser.
No, but you can specify that only logged users can use the sharing features, or the Web-app generation feature.
Did you edit your .htaccess file adding the line specified in the Plugin's Settings? Other explanation may be that you need to let it download the whole content after opening the icon. Delete the icon / clean cache and download again the app.
You need to enable this feature in the Settings menu of the panel.
Yes, just follow these steps: