Sous is indeed odd here. If you want to keep it, that would be sous l’égide de mon professeur. A more usual expression is avec comme professeur Madame Siu.

En dehors de l’etudie is hard to read due to a missing accent and a grammatical error. I guess you want to write En dehors de l’étudier but this is partially contradictory given the fact learning the culture, listening to music and reading the media is still étudier. You might want to say: En plus des cours de français, …

There are also a dozen of typos and mistakes in the remaining of your paragraph. I would advise you to use the suggestions already posted as comments to improve it.