Digestion and Absorption

The pharynx is a common passage for food and air; the oesophagus and the trachea both open into it.
The opening of the wind pipe is the glottis. During swallowing a cartilaginous flap, the epiglottis, covers the glottis and prevents the entry of food into the wind pipe.
If the epiglottis does not close the glottis properly, for example when a person talks or laughs while eating, food particles enter the wind pipe.
This triggers the cough reflex to expel the food.
Hence the coughing is due to improper movement of the epiglottis.

Milk proteins are first acted upon in the stomach, by the enzymes of gastric juice.
Rennin is the milk-coagulating proteolytic enzyme found in the gastric juice of infants; in calves it is the main milk-digesting enzyme.
In adult humans rennin is absent, and the initial step in the digestion of milk protein (casein) is carried out by pepsin in the acidic medium of the stomach.
Trypsin acts later, in the small intestine, and lipase acts on fats, not on milk protein.
The answer accepted in the key is pepsin.
Note: some books give rennin for this question on the basis of its presence in infants; the key of the source PDF (pepsin) is retained here.