Is it permissible to raise the external and internal volume of mosques, to excessively use microphones, to play the radio for a long time before the prayer, and sometimes to broadcast a woman's voice through it?

It is permissible to play the radio with loudspeakers unless it is intended for worship, and does not involve harm or disturbance to Muslims. Otherwise, it is forbidden, especially if it includes women's voices.

As for using loudspeakers in prayer, it is permissible out of necessity only inside the mosque, provided that it does not harm those outside. If the imam's voice reaches the worshipers, there is no justification for using them, especially if it distracts the imam from the sunnah (recommended practices) of prayer.

It is not permissible to use external loudspeakers for prayer due to the harm and disturbance it causes to the people in houses and other mosques. The Prophet, peace and blessings be upon him, forbade raising one's voice in recitation to the extent that it harms others. When benefits and harms conflict, warding off harms takes precedence over achieving benefits.