Based on the given information, if no friction acts on a diver during a dive, then the only force acting on the diver is gravity. This means that the mechanical energy of the system is conserved.
Option A: The total mechanical energy of the system increases - This statement is not true because mechanical energy is conserved when no external forces, such as friction, are acting on the system.
Option B: Potential energy can be converted into kinetic energy but not vice versa - This statement is not true. In the absence of friction, potential energy can be converted into kinetic energy and vice versa because mechanical energy is conserved.
Option C: (KE + PE) beginning = (KE + PE) end - This statement is true. As mechanical energy is conserved when no external forces are acting, the sum of kinetic energy and potential energy at the beginning of the dive should be equal to the sum of kinetic energy and potential energy at the end of the dive.
Therefore, the correct answer is C. (KE + PE) beginning = (KE + PE) end.