The flashbacks are meant to be ones of the endless repeating Junes before that one. As Rika said at the end "I'll play along with this endless June for as long as you want."
Keichi thinks it's some 'alternate universe' but most of the citizens of Hinamizawa don't know about the repearting June. Rika is meant to be one of the keys to that endless June I believe.
He remembers them because they relate to Rena and for some it takes longer than others to remember. His situation was the 'disease' which causes paranoia (I believe)
The maggots incident Rena believes is that either Oyashiro-sama is really punishing her because she left the village or maybe it's because of the paranoia the disease causes. It may have something to do with Takano's theory, but then again, they ARE just theories. Rena went with that theory as it was the closest thing to the maggot incident. She even was desperate enough to believe it was aliens.
Keep in mind there are 8 arcs - 4 question arcs and 4 answers arcs. In the second season, if there is one (or a remake) they will prehaps be playing only 2 arcs.