What are the circumstances in which a man is prohibited from marrying until he fulfills certain obligations, and what are the evidences for this from the sayings of scholars and fatwas, along with mention of some sources?

The waiting period (iddah (definition)) in the Islamic legal sense is not obligatory for a man. Rather, he is permitted to marry immediately after separating from his wife, unless there is a legal impediment. Such impediments include his desire to marry her sister, paternal aunt, or maternal aunt, or if he divorced his fourth wife and wishes to marry another. In these cases, he must wait until her iddah period concludes, regardless of whether the divorce was revocable or irrevocable (according to the majority of scholars). This is because a woman in a revocable divorce is still considered to be in the status of a wife.