What is the ruling on a binding judicial decision? And what are the conditions for its formation? And is it a prerequisite for it to be in a formally filed lawsuit?

A judge's ruling is what he issues between litigants concerning a matter brought before him. If he rules something, it becomes binding for execution. No one else is permitted to overturn this ruling unless it contradicts a text or a consensus. As for a fatwa, it is not a binding ruling.