planet - Does earth have retrograde motion?

It does not have a retrograde motion. It has a prograde rotation, and a prograde orbit of the Sun.

If you were to look down on the solar system from far above the north pole you would see the planets orbiting the sun counter-clockwise. And the planets, including the earth also spinning counter clockwise. The Moon also orbits the Earth counter-clockwise. All this motion is in the same direction, and called prograde.

There are a couple of exceptions: Venus spins clockwise. Venus spins in a retrograde motion. There is a moon of Neptune, Triton, that orbits retrograde. Uranus spins on its side.

The reason is that most objects rotate the same way is that the planets and the sun formed out of the same cloud of gas and so have the same direction of spin.

There is another sense of "retrograde". As the Earth overtakes the other planets they seem to move backwards in the sky for a while.

From the inner planets, Earth would appear to move rather like mars, with periods of retrograde motion. From the outer planets Earth would move like Venus, moving from being a "morning star" to an "Evening star".