Question

Can a motion in rest be also in a constant motion

Answer 1

Rest and motion are the relative terms because they depend on the observer's frame of reference. So if two different observers are not at rest with respect to each other, then they too get different results when they observe the motion or rest of a body.

A rock sitting on the ground is at rest with respect to the earth, but the earth is turning and moving around the sun and the sun is moving through space, etc, so we have to state the framework. In that sense a body can be at rest and in motion at the same time. But not both in the same framework.