Is air pressure higher at higher elevations?

Lower. There is less air pressure pushing down on you, than say, a deep sea diver

At lower elevations, more air is pushing down because of gravity. Just as if one were to go 100 ft below a lake vs. 10 feet. There is more air, just as there was more water above you in the lake,...

Air pressure starts to go away

Because cold air is more dense, and also contains less water vapour.

Increasing altitude decreases air pressure. In other words, they are an inverse relationship -- as one goes up, the other goes down. This is why when low-altitude dwellers like along the coastlines...