Why is water added to the reaction product dissolved in ethoxyethane (diethylether)? 

To remove water-soluble impurities.

What can you say about the partition coefficient, K, where K = (concentration of reaction product in ethoxyethane)/(concentration of reaction product in water)?

The value of K will be high so that most of the reaction product remains dissolved in the ethoxyethane layer rather than dissolving in water.

What determines which is the lower and which is the upper layer in the separating funnel?

The liquid with the higher density will form the lower layer and the liquid with the lower density will form the upper layer.

What must the student do before running the lower layer into a clean conical flask?

The student must remove the stopper so that the liquid can run out of the separating funnel.

How can the student tell when sufficient drying agent has been added to the ethoxyethane layer?

The drying agent forms a 'snowstorm' effect when the flask is shaken. When insufficient drying agent is added it tends to 'clump' together.