The reason for hardship in the Muslim world during the time of the European Middle Ages is best described by the first response: Mongol armies from central Asia repeatedly invaded and conquered parts of the Muslim world. The Mongol invasions had a significant impact on many regions, leading to destruction and instability.
While the Crusades and Byzantine attempts at conversion were also factors of conflict, the direct and widespread devastation caused by the Mongol invasions was a more prominent reason for hardship during this period. The other options regarding European Crusaders and Byzantine efforts are less accurate in terms of their overall impact on the Muslim world compared to the Mongol invasions.