What is the ruling on the Imam and Mu'adhin repeating certain surahs and verses, and their delay in observing the prayer and adhan times? Does the hadith, "And a people's Imam when they dislike him," apply to them? And is it beneficial to inform them of this fatwa?

You can contact the responsible authorities to fix the mosque's maintenance issues and air conditioning, and you will be greatly rewarded for it. What you mentioned about the Imam and the Muezzin does not necessitate disliking them; there is no prohibition in him mastering some parts and reciting them frequently, and the entire Qur’an is good. You can ask him to change the parts gently and kindly. There is no harm in reciting some surahs at specific times if their Sunnah status is not believed. You did not mention anything about the Imam that would necessitate disliking him to the extent that he falls under the warning "whoever leads people in prayer while they dislike him," unless the dislike is justified. Some of what you criticized the Imam for doing is Sunnah, such as prolonging the sitting between the two prostrations, and some is not, such as prolonging the first tashahhud. All of these are minor issues that can be rectified through sincere advice. And an exhortation to unite hearts and gather the word.