Is the questioner considered a resident in his father's house in the capital or at his place of work? And is it permissible for him to shorten prayers in either of these two places, or only while traveling? And if he is required to shorten prayers, what is the duration of the shortening?

The homeland recognized by Islamic law is the place where one intends to reside permanently. If you intend to reside permanently in your place of work, then it is a homeland for you. If you travel to your father's house and intend to stay for four days or more, then it is not permissible for you to shorten or combine prayers. However, it is permissible for you to do so while traveling to your homeland and returning to your father's house.