(a) The correct option is (A).
The pressure of the water in the lake increases with depth. As the balloon sinks deeper inside the lake, the pressure of the water is increase. This makes the force acting normally on the air molecules inside the balloon increases with depth. Thus, the air pressure inside the balloon will also increase. Therefore, option (A) is correct.
Other options are rules out.
(b) The correct option is (A).
It is found that the pressure start increasing once the balloon start sinking. From ideal gas equation, the pressure of the gas times the volume remains constant at constant temperature. Consider the temperature of the water in the lake to be constant. This means there would be decrease in the volume of the balloon. This means the volume of the air molecules will also decrease. It is also known that density is mass per unit volume. If the volume of the air molecule is decreased, than the density of the air molecule is increase. As the density of the balloon and rock remain constant. The increase in the density of the balloon, rock and air molecules also increases. Therefore, option (A) is correct.
Other options are rules out.
(c) The correct option is (A).
The force acting on the balloon, air and rock is the pressure exerted by the water times the surface area. Now, the net force acting is equal to the difference in the force on the balloon, air and rock in air and the buoyant force acting on them. As it goes deeper, the magnitude of the net force will start increasing.
Therefore, option (A) is correct.
Other options are rules out.