Does secular education coincide with Islam?

[ardianto]

what about hadiths, Fiqh and other Islamic topics, Do they teach them in Institutions you went to?

It's taught only in Islamic science faculties like faculty of sharia, tarbiyah, ushuluddin, etc. In Indonesia, Islamic university is university that has Islamic science faculties and general science faculties like engineering, economics, etc. If it has only Islamic science faculties, then it's called Islamic institute or Islamic higher school.

how is the education system in general in Indonesia (maths, science, history and literature)?

Religions are taught in Indonesian schools, in accordance of the student's faith. Muslims students learn Islam, Christian students learn Christianity, etc. But other subjects like math, biology, etc, are not attached to any religion.