Is a man's intention regarding divorce determined by the spoken word or by what he actually intends, for example: Does divorce occur if someone announces the arrival of an absent person with the divorcer's intention to convey the news in any way, or if the divorcer intends to spend the night sleeping and the wife spends the night at her family's house without sleeping?

What you have mentioned is an oath of divorce, and intention is considered therein. It specifies a general term and generalizes a specific term. An oath is based on the intention of the swearer. If he intends by his oath something that it can bear, then his oath is directed to it, whether it aligns with the apparent meaning of the word or contradicts it. Among the contradictions is for him to intend a specific meaning by a general term, or to intend to do or not do something at a specific time, or to intend by his oath something other than what the listener understands from it. So, if someone swears by divorce that his wife will not leave, and she leaves in a manner different from what he intended, he has not broken his oath. However, if someone explicitly utters the word divorce, his intention not to cause the divorce to occur is not considered.