All the nasties go to sleep at night. When you pause a game, the day/night timer still runs. Thus it is possible to play only during the safe night periods, and pausing the game during the dangerous daylight.
MISSION 1: Feed the monkey on your back bananas. Eventually, this will give him a bad case of diarrhoea, and he'll run off to a secluded spot.
MISSION 2: Reunite the lion cub with his mum. Look in the tree trunks.
MISSION 3: Save a sick native, buy medicine.