lets get this done quickly :)
1.) I guess they have made an own theme and named it that way.
2.) In the editor you have a "readmore" tag if you click this you will insert a special line / markup. Now your theme nees a call for this line "Excerpts (teasers) can be shown on WordPress through two methods:
The first, keeping the the_content() template tag and inserting a quicktag called more at your desired "cut-off" point when editing the post. The second, by replacing the the_content() template tag with the_excerpt()." Here is all you need: Link to wordpress documentation the excerpt
3.) There are quite a lot of ways to do that. You could order posts by popularity by the number of comments or the number of views or the number of shares. There a loads of tutorials on the web to do so. It's so simple it would be sad to use a plugin AND: you could learn a lot from it... tutorial by view is here: http://www.wpbeginner.com/wp-tutorials/how-to-track-popular-posts-by-views-in-wordpress-without-a-plugin/ tutorial by number of comments is here: http://www.jafaloo.com/how-to-display-popular-posts-in-wordpress/
all the best fabian