What is the ruling on naming a child "Munira," is it pronounced with a kasra on the mim or a damma, and was this name present during the time of the Messenger of Allah, may Allah bless him and grant him peace?

There is no religious impediment to being named "Munira." It is an active participle from "anara," meaning "illuminating" or "bright," and is used to describe anything that illuminates, such as the sun. It is also the name of a place near Medina. There is no religious text that prohibits naming with it.