Mushi Random is probably a reference to Kokoro Connect; almost all of the volumes are subtitled "[something] Random".
No idea for Tsuki no Insurōru
Shizuku Lost might be a reference to the chapter "Sodachi Lost" from Owarimonogatari? Though it's possible that is itself a reference to something...
This line on page 20 almost sounds like it could be the author alluding to some external force (maybe the publisher, or something else) forcing them to speed up the pace of story.
Theoretically, it's entirely possible that more than one of the girls is real. All the teacher said in the beginning was that he knew there were four love-eaters among the newly students. So there's not really any reason that all four of them have to be among the five girls who confessed to him.