Is the use of external loudspeakers in the mosque to broadcast audible and inaudible prayers, lessons, sermons, and announcements, which causes disturbance to neighbors and prevents them from using their phones or opening their windows, considered permissible (halal) or forbidden (haram)?

The use of loudspeakers outside the mosque is permissible for the Adhan (definition) (call to prayer) and for announcing deaths. There is nothing in Islamic law that prohibits their use for prayers and lessons, but it is preferable to avoid them if their use causes annoyance to neighbors. The questioner is advised to thank Allah for the proximity of the mosque to him and for his eagerness to pray therein and benefit from its religious knowledge, and to be among those who maintain it, for "The mosques of Allah are only to be maintained by those who believe in Allah and the Last Day." He is also advised to contact the Imam and the prominent figures in the neighborhood to explain the matter to them gently.