Is it permissible to pray after the first call to prayer in an area with several mosques, each calling to prayer at a different time, or must one wait for the call to prayer from all mosques, and what is the best time to pray, knowing that another mosque might call to prayer while one is beginning to pray?

It is recommended to hasten the prayer after verifying that its time has begun, based on the hadith of Umm Farwah: "Prayer at the beginning of its time." If you do not have knowledge of the beginning of the time, then use a calendar. It is permissible to follow a just muezzin who is knowledgeable of the time, for the Prophet, peace and blessings be upon him, said: "The muezzins are trustworthy." There is no need to wait for a second or third muezzin; the important thing is to ascertain that the time has begun.