Ice at night is not unhealthy - unless you're one of those people who easily get an upset stomach. Another one of those weird Japanese superstitions like getting sick just from getting wet.
Also, most of those (probably all?) are real products, I recognize most of them from Japanese stores. In particular, the one with the guy with the giant mouth is Garigari-kun. Gari Gari is the sfx of crunching ice with your teeth, and Haruka uses that sfx a couple times while crunching down on it.
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GARI!