Is it permissible for a person residing for work in Minya—200 km from his hometown—from Sunday to Thursday, to shorten prayers (qasr) in Minya or in his hometown of Fayoum?

You are not permitted to shorten prayers (qasr) in Fayoum because it is your hometown. However, in the country you travel to, you are permitted to shorten prayers if you do not intend to reside there for a full four days, excluding the days of entry and exit, according to the Shafi'i and Maliki schools. In this case, if you enter the town on a Sunday and depart on a Thursday, you may shorten prayers. As for the Hanafis, they hold that the period permitting the concessions of travel is fifteen days. Imam Ahmad, in one narration, believes the period is four days, including the days of entry and exit, while in another narration, he considers the period that obligates a traveler to pray in full if it exceeds twenty-one prayers.