Is it cultural difference I see? Where I live saying to someone to close their eyes and open their mouth would be obvious sign that you want them to taste something or perhaps do a prank on them.
@zeror3 Even in the other mangas, the prelude to one of those kiss moments is just to have the other person close their eyes. Nothing about opening their mouth.
The exception I can think of is maybe if it's a kiss that involves tongue but those tend to be different mangas.
The scooter that Hajime-san was riding at the beginning is called Honda Motocompo. The first gen Honda City had it as an option. Basically the scooter can folds itself and it was big enough to fit in the trunk.