What entropy change occurs, if any, when a pack of 52 cards is shuffled into one particular arrangement? Is the concept of entropy appropriate in this case? If so, explain how one could get useful cooling by carrying out this process adiabatically.

Entropy is often associated with disorder and the second law of thermodynamics is sometimes cast as a statement that the disorder of a closed system always increases. In accordance with second law of thermodynamics, the entropy of the universe tends to a maximum. In this case, due to shuffling, the system will go into more disordered state. Since entropy measures the state of disorder, therefore the entropy of the system will increase.
Yes, the concept of entropy is appropriate in this case.
The process in which change in pressure, volume and temperature takes place without any heat entering or leaving the system is called adiabatic change. Whenever there is a process which takes place suddenly, it should be taken as an adiabatic change. The word suddenly implies that the system hardly finds time to get the heat exchanged with the surroundings. Cooling is caused by the adiabatic process. Keeping the exchange of heat with surrounding remains constant but exchanging the matter, you could get useful cooling by carrying out this process adiabatically