What is the ruling on a man listening to a woman's chanting (nasheed), and the ruling on a woman listening to a nasheed chanted by a man? And why is the first not permissible while the second is? And is there a problem if nasheeds are distributed such that women chant only for women and men chant only for men?

It is impermissible for a man to listen to a woman's nashīd (recitation/chant) due to the fitnah (temptation) it entails. As for women listening to a man's inshād, there is no objection to it if it adheres to the শরعي (Sharīʿah-compliant) regulations, based on what was narrated by Anas ibn Malik, that the Prophet (peace and blessings be upon him) said to his camel driver, Anjashah: "Slow down, Anjashah! Do not break the glass vessels!" meaning the women. It is preferable for both men and women to limit themselves to listening to nashīd of their own gender.