What is the ruling on shortening (qasr) and completing (itmam) prayers in the aforementioned journeys, and is it obligatory to make up the days during which prayers were shortened by mistake?

If a traveler intends to stay for four days, their journey is considered interrupted, and they are obligated to complete the four-rak'ah prayers. This is the view of the majority of scholars. If the duration of stay is less than four days, then shortening the prayers is permissible. If a traveler intends to stay for four days or more and then shortens the prayer, they are obligated to repeat it according to the majority. Shaykh al-Islam Ibn Taymiyyah, however, held the view that a traveler may shorten prayers as long as they have not intended an absolute (indefinite) stay. Upon returning to one's village, the journey is considered ended.