Is adopting the view that there is no connection between the prayer of the Imam and that of the worshiper considered following dispensations, and is it obligatory to adhere to a specific madhhab?

Do not listen to the words of this person. Rather, adhere to the mosques and witness the congregational prayers therein, for in that is a great reward. The default is the validity of the Muslims' prayers, so rule that the prayers of all imams are valid unless you are certain of the contrary. The default is that the muezzins call the adhan at the correct time, and acting upon their adhan and reliable calendars is permissible and there is no harm in it. Abandon those doubts. It is not obligatory to follow a specific madhhab; rather, you imitate whomever you trust among the people of knowledge.