What are the consequences for someone who swore not to do something for a certain period and then did it, and what is the difference between an oath (half) and a vow (nadhr), and is expiation (kaffarah) required of him?

What you said is considered a binding oath, and if you break it, you must offer an expiation for an oath, which is: feeding ten poor people, or clothing them, or freeing a slave. If you cannot find any of these, then you must fast for three days. The difference between an oath and a vow is that an oath is an affirmation and confirmation of something that is not obligatory to occur, and it is only binding when made by one of Allah's names or attributes. As for a vow, it is the commitment of a responsible Muslim to an act of worship.