What is the difference between Quran teaching and Islamic studies? Then there is also arabic teaching...?

Simply - Arabic is the language of the Quran Islamic Studies is the study of History of Islamic civilisation and Quranic teaching is the study of the holy book the Quran and read in Arabic and meanings of the verses explained.

Islamic studies is a broader topic, it can include learning Qur'an as well as Arabic (the latter for better understanding of the original texts which were in Arabic language). Islamic studies includes Fiqh (understanding of the rulings and their application), Aqeedah (the creed/methodology), Hadith (the sayings of the Prophet peace be upon Him) and so on.

Islamic studies includes teaching of islamic history, seerah, fiqh and covers all aspects of Islam. It also includes studying the explanation of Quran. However Quran study will only focus on the study of Holy Quran. It includes reading the Quran in Arabic as well as understanding it's meaning. I you want to discuss in detail message me.