(a) It is true that Evaporation produces cooling.
Evaporation is a surface phenomenon. Since some heat energy is taken from the surrounding during the process of evaporation. The particles of the liquid absorb energy from the surrounding to regain the energy lost during evaporation. This absorption of energy from the surroundings make the surroundings cold producing a cooling effect.

(b) Its true that the rate of evaporation of an aqueous solution decreases with increase in humidity.

The amount of water vapour present in the air is called Humidity. At a given temperature, the air around us cannot hold more than a definite amount of water vapour. If the amount of water in air is already high, the rate of evaporation decreases. As a result, the rate of evaporation of an aqueous solution decreases with increase in humidity.

(c) Yes, Sponge is a solid though it is compressible.
Sponge has a lot of small holes in it. Air is trapped inside these minute holes. When we press the sponge, air is expelled out and we can compress it. The sponge remains in that compressed shape until we apply force on it. When we release it, the air reoccupies its minute holes and the sponge regains its original shape.