Where is a planet when it is moving most rapidly in its orbit?

Any object in an elliptical orbit - this would include every planet and natural satellite - is moving fastest when it is closest to the "primary object" around which it orbits; the Sun in the case of the planets, and each planet in the case of a moon.

The Earth reaches perihelion, its closest point of approach to the Sun, on January 4 each year, so that's the day at which the Earth is moving fastest in its orbit.