I'm no expert, but here's my take on a few examples:
c07: "feeding other people's kids" - I think Hina wanted to emphasize that Rei is "someone else's kid", and you don't address a stranger by their first name (much less with a "-chan" suffix).
c13 - Rei is talking to Takahashi and was about to refer to Hina as "Hina-chan", then stopping to correct himself to "Kawamoto-san". This might be more appropriate because Takashashi calls Hina "Kawamoto" and not by her first name. "-san" is added for politeness, since Rei is speaking to someone he just met.
On the next page, Hina thanks Rei as "Kiriyama-kun" - you can see she's really flustered/happy that Rei created this opportunity for her to have contact with Takahashi - so it might be out of a combination of shock and utter respect for Rei that she uses the more polite address. Or it could also be a follow-up to Rei's "Kawamoto-san", but then Rei has already switched back to "Hina-chan" since it's just the two of them. Of course after dinner (on the same page), she's back to calling him "Rei-chan".
In Japanese, there's this concept of "inner circle" vs. "outer circle". "Inner circle" are usually your family and close friends. "Outer circle" is everybody else. I think in the first couple of chapters, Hina was still addressing Rei with "-kun", and gradually she switched to "Rei-chan". This might indicate Rei's transition from Hina's "outer circle" to her "inner circle".