i) Water droplets will form where a warmer environment meets a cooler surface as shown visually in (ii) diagram.
The water in the cup is cold, which also cools the surface of the glass cup.
Because the air around the cup is room temperature, which is warmer than the surface of the cup, the warmer water vapour in the air outside the cup will condense on the cooler outer surface of the cup.

ii) There must be a rather significant difference in the temperature between the glass and the air around the glass for condensation to take place.
Since cold water is in the cup, the surface of the cup will be cold.
However, this cup is placed in the refrigerator and the air in the refrigerator is cold.
Since the glass is cold, and the air around the glass is also cold because it is inside a refrigerator, there is not a significant temperature difference between the surface of the cup and the air around it.
Therefore no condensation will take place.

In short:
The air in the refrigerator has a similar temperature to the temperature of the cup with cold water. No condensation will take place as the temperature difference is too small.