What is the specified distance for shortening prayers (qasr), and is there a specific duration for a traveler after their arrival to continue praying shortened? And what is the authenticity of the hadith: "Whoever prays four rak'ahs while traveling must repeat the prayer," and the hadith about the Prophet (peace be upon him) praying shortened in Mina for eight years?

Islam permits a traveler on a lawful journey to shorten the four-rak'ah prayers. Jurists' opinions varied regarding the duration of shortening. Some hold that a traveler may shorten prayers as long as they do not intend to reside permanently, even if they stay for years. This is the preponderant opinion and the practice of the Salaf (early Muslims). Others believe that shortening is permissible for up to eighteen days, while some hold that the prayer should be completed. As for the two traditions mentioned, the first concerning Ibn Mas'ud regarding someone who prayed four rak'ahs while traveling, Al-Haythami stated that its chain of narration is disconnected. Even if authentic, it might represent one of his opinions or signify desirability. As for 'Uthman's completion of prayers in Mina, he had justifications, including his view that shortening was specific to those actively journeying, or that he believed the Prophet, peace and blessings be upon him, chose the easier path for his Ummah, while he chose the stricter one, or that he intended to teach the Bedouins that the prayer consists of four rak'ahs. As for the second tradition about 'Imran ibn Husayn, it was narrated by Muslim and indicates the disagreement among the Companions regarding the issue of shortening and completing prayers. The majority of jurists hold that shortening is desirable, not obligatory.