DEfinitely insulate the void in the ceiling. You can probably get some thin batt insulation at a big box store. That can be pushed into the void with sticks or wire. If you source 3 1/2 batt insulation, that can be divided into thinner pieces. Wear gloves.
Basically, you have a condensation point at the skylight. It is an indication of the humidity being too high. Venting is the best solution. You can also insulate underneath the sky light but you'll lose light and the insulation must be sealed totally. Otherwise, you'll have condensation again on the inside of the skylight. You could choose to seal the skylight opening with a transparent material like acrylic. Again, sealing all areas is necessary to eliminate condensation on the skylight.