does air exert pressure?

Yes, this is why when you go up in the mountains you have to rise slowly, because the air pressure is different. (In the case of mountains, the air becomes thinner so your lungs have to get used to taking in less oxygen per intake) and closer to the ground you have more air above you pushing down (like gravity) I agree with Dedeea's answer, but I wonder if this may also help clear any confusion ;)

Yes. Air exert pressure on bodies and objects that surround them: this is called atmospheric pressure. Is this the answer you were searching for?