What is the ruling on changing the time of the second Fajr adhan based on a specific research, what is the role of the imam when the common people object to this change, and is the imam responsible for what the muezzin does when he abandons the adhan in response to the common people?

The first Adhan before Fajr is a Sunnah, for those who wish to perform Qiyam al-Layl to wake up. It does not necessitate prayer nor does it prohibit food for the fasting person, as the Prophet, peace and blessings be upon him, said: "Indeed, Bilal calls the Adhan at night, so eat and drink until Ibn Umm Maktum calls the Adhan." Some scholars have disliked the Adhan before Fajr in Ramadan so as not to confuse those who are fasting, except for those who have two muezzins. If the practice of having two Adhans for Fajr would cause confusion or discord, then the correct approach is to abandon it to prevent such discord.