It's not very common. One reason could be that she might have forgotten her shoes in the gym locker. Another possibility is that she has some discomfort in her shoes and prefers to go barefoot for a while. Maybe she's in a hurry and didn't have time to put her shoes back on properly.
No, it's not common. In most schools, there are dress codes that require students to wear proper footwear for safety and hygiene reasons. In the story, if she is barefoot, it's likely an exception due to the reasons mentioned before like losing shoes or having an injury.
There's no way to tell for sure who the barefoot girl is without more of the story. She could be a fictional character created to teach a lesson, like a poor girl from a small village who values the shoes she has and is distraught when she loses them.
It could be that someone played a prank on her and hid her shoes. Some students like to do naughty things like that. There's also a possibility that her shoes were old and the sole got detached suddenly, making it impossible for her to wear them.
Maybe she lost her shoes. It could be that she was playing too hard during recess and her shoes got misplaced. So she had to be barefoot in school until she found them or got a new pair.
Maybe she would be teased by her friends who would tickle her feet for forgetting. And she'd be laughing and trying to get away while also being a bit embarrassed about the forgotten shoes.
There was this barefoot girl who forgot her gym shoes. When she told her friends about it, they decided to have some fun. One of them started to tickle her feet as a joke. She squealed with laughter. Later, they found an old pair of shoes in the lost and found for her to use in the gym.