Regarding the curvature of the Earth
About curvature, you can see it. Just look at a ship some hundred meters away: you'll notice if you are careful that you can not see where the ship touches water.

You can see at http://mathcentral.uregina.ca/qq/database/QQ.09.97/dyck2.html that the curvature is 8 inches per mile.

On the other hand, about rotation, planes do actually take advantage of earth rotation, but not directly. This was answered in https://physics.stackexchange.com/questions/16390/does-the-rotation-of-the-earth-dramatically-affect-airplane-flight-time