Does the ruling of a traveler or a resident apply to me, and is it permissible for me to combine prayers due to work circumstances, and is it permissible for me to shorten or combine prayers, or both, throughout my four-year period of study in Europe while residing there with my family?

As long as you are residing in that country, you are not allowed to shorten the prayers (qasr), because the ruling of travel ceases as soon as one intends to reside for four days or more according to the majority of scholars, or for a period in which one performs more than twenty prayers according to the Hanbalis, or fifteen days including the day of entry according to the Hanafis.

If there is hardship or difficulty in not combining the prayers (jama‘), then it is permissible for you to combine the two prayers.