Why does Minori have a flower on her head?
This is a little tenuous, but the kanji in Minori's name seem to have kind of a plant theme to them. In Japanese, her name is written 櫛枝 実乃梨 (Kushieda Minori). The kanji 枝, read eda, has the meanings "bough", "branch", "twig". The kanji 梨, read as ri, means "pear tree". That could be why they chose to symbolize her with a flower.

Denshi Jisho page on the kanji in Minori's name.