When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. if the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? i think the answer is 4p but i don't know why.

Pressure is (weight of the box) / (area under the bottom of the box). Neither of those quantities depends on the area of whatever is under the box. You could move the box from the deck of a battleship and put it on the kitchen table. The pressure it exerts doesn't change.

the answer is false. this is because for ice to melt, it requires latent heat of melting. latent heat means heat energy required to change phase without any increase in temperatures. therefore, the ice will take energy from the environment to melt hence atmospheric temperatures will reduce.