What is the correct view on the issue of determining the time for establishing Fajr prayer after the Adhan: Is it to prioritize caution and precaution by delaying the establishment for 25 minutes as the Imam sees fit, or is it to consider the congregants' interest by not exceeding 20 minutes to avoid disunity? And what is the minimum duration in minutes after the Adhan (according to the calendar) after which Fajr prayer can be established?

There is no specific time limit between the Adhan (definition) and the Iqama. The governing principle is that the duration should be sufficient for people to prepare for prayer and gather. It was narrated that the Prophet, peace and blessings be upon him, told Bilal to leave enough time between the Adhan and the Iqama for people's essential needs. The Imam of the mosque estimates this based on the congregation's readiness, without causing undue delay that would lead to hardship for them, because offering prayer at the beginning of its time is better. The Imam should be gentle with the congregants; otherwise, his prayer might not be accepted if he leads people who dislike him due to his harshness towards them.