A stationary target that is 1/20th the size of an aircraft carrier, mind you.
It would only make sense that it is capable of this. Ships don't sit still when targeted by missiles, and Iranian engineers know this.
Strictly speaking, the Khalij Fars is actually a
quasi-ballistic missile. It follows a much shallower trajectory, which allows it to retain aerodynamic control in flight. As for aerodynamic control, it has 3 sets of fins (1 at the nose, 2 at the tail), at least 2 of which (including the nose fins) are moveable. In comparison to most ballistic missiles (including most Iranian ones) which have just 1 set of fins at the tail.
All images of the Fateh series of missiles indicate that the warhead does not separate from the main fuselage, though there is some speculation that the most advanced land variant, the Zolfiqar missile, may have a seperating warhead.
Whole missile, not just warhead.