If a women run course on Islam in a masjid, Can she still run courses in masjid during the monthly cycles.Is the answer same even if she thought quran.Jazzakallah khairun

It is not permissible for a woman during her menses to enter the Musjid. (Raddul Mukhtaar vol.1 pg.213/214; Rashidiyya)

If a woman is teaching the Qur'aan to girls, then in such a case it will be permissible for her to spell out the words. When she is teaching them to read with fluency, she should not recite the entire verse, but should read one or two words at a time and after every word or two, she should break her breath. She should teach them to read fluently by stopping regularly (herself). (Bahishti Zewar pg.183)

And Allah Ta'ala Knows Best

Mufti Ebrahim Desai