The circulation in the atmosphere is driven by the unequal (latitudinal dependence) of the solar flux input. Since the equator gets more of the suns radiant energy than the poles due to the tilt of the Earth's spin axis (the OBLIQUITY), the redistribution of this heat, from equator to poles, is a primary driver of general circulation. In addition, the rotation of the earth gives rise to a force called the Coriolis force. Coriolis Effect is a deflection of moving objects when the motion is described relative to a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right.

So it is this effect, together with the Hadley circulation---from equator to poles that gives rise to the major wind belts. Now, at our latitude the general flow is indeed as you note from WEST TO EAST. However, at lower latitudes the flow is OPPOSITE! This is because at the equator to pole Hadley circulation is not one large gyre. Instead due to Earth rotation the Hadley gyre is actually broken into three pieces, and at the surface the low latitude flow is North to South and hence the Coriolis turns things to the East (NORTHEAST TRADE WINDS), whereas at our latitude the opposite is true. The surface Hadley flow is South to North and hence Coriolis turns the flow to the East (West to East zonal flow).

This is an interesting question. The west to east movement of weather systems is a consequence of two phenomena: 1) there is a gradient in the speed at which matter travels as a function of latitude, 2) warm air from the equator rises and moves toward the poles. The first point is that someone standing at the equator is moving at a faster speed relative to the Earth's axis than someone standing at one of the poles. As air travels around the Earth, its momentum is conserved, so even though it is moving northward or southward toward one of the poles, it maintains its eastward direction.

Friction with the geological features on the Earth's surface may cause local slowing or even directional changes in the wind, but even the highest mountain on Earth only rises to ~5.5 miles above sea level, but most trees and mountains exist at much lower heights relative to the Earth's surface. On the other hand, the troposphere, where weather occurs, extends anywhere from 5-12 miles above sea level, so on average winds in the upper troposphere are not very affected by friction of air with the Earth's surface. I hope this helps!

The answer depends on the latitude. The atmosphere circulates north-to-south as well as being in contact with the ground, which means that there is an "average" speed with which the atmosphere is rotating. In the tropics, the winds blow from east to west more-or-less as you describe, but in the temperate parts of the globe, the Earth isn't moving so fast because you are closer to the Earth's axis of rotation, with the result that the winds tend to blow from the West instead of from the East.