To clarfy things in north africa, the abbasids gave power to the aghlabids in north africa in the early 9th century where they ruled from tunisia on behalf of the abbasid caliph, from there in the mid 9th century the tulunids ruled as independent in egypt. The fatimids in 910 overthrew the aghlabids and ruled from tunisia and it wasn't until al-Muizz in 969 conquered egypt and rule from there. Salah al-Din was a zangid general who overthrew the fatimids and founded his own ayyubid dynasty.
This is quite correct. And accordingly I think the Fatimids are the ones whose starting and ending dates lye within the scenarios time frame. Their rule actually extended into the eastern coast of the Mediterranean up to Syria in times.