The plot: Simple, it's a look at Rika and Terada's life and what's going on. It's also about problems they might have...adult-life issues. It's pretty straightforward, so yeah...you just might be slow on that one.
Regarding Yamazaki-kun. Takashi and Yamazaki can BOTH be used as given names or as surnames.(Trust me, I've known both!) In the anime, Terada has refered to him as 'Takashi' during role call--and he also calls him 'Yamazaki'. So, there is some disagreement. It is my belief that Chiharu is NOT calling her boyfriend by his last name. The boy in question is called 'Yamazaki' by people he calls by their given names (ex. Rika-chan, Chiharu-chan). So I stand by my use of Yamazaki as a first name. Besides, it's what I've been calling him in all of the Third Arc stories...I'm not changing it now.