What are licit and illicit marriages and their respective consequences, and what are licit and illicit divorces and their respective rulings?

There is no term in Sharia called "bid'i marriage" (innovated marriage). Marriage is either valid, if its conditions and pillars are met, or it is void/corrupt if they are not met. As for divorce, it is divided into Sunnah (prophetic) divorce (which occurs during a period of purity in which no intercourse took place, or during pregnancy) and bid'i (innovated) divorce (which occurs during menstruation or a period of purity in which intercourse took place). Bid'i divorce is valid, but the one who pronounces it incurs a sin.