Moving the stick forward commands a nose down pitch input, which reduces the angle of attack of the wing. The immediate aerodynamic consequence is that lift decreases, so the aeroplane begins to descend and the flight path inclines downward. 

Because thrust is unchanged and the flight path is now descending, a component of the weight acts along the direction of motion and accelerates the aircraft, so the airspeed rises.

At the same time, the increasing descent angle directly translates into an increasing sink rate (vertical speed downward), since sink rate is approximately equal to true airspeed multiplied by the sine of the descent angle. 

The speed increases and the sink rate increases → CORRECT. Pushing the stick forward lowers the nose, reduces the angle of attack and establishes a descending flight path. The aircraft picks up speed because a component of its weight now acts along the direction of motion, and the sink rate increases because the flight path is inclined downward. This is the classic trade of altitude for speed that follows any uncorrected nose down input.

The speed decreases and the sink rate increases → INCORRECT. A nose down input does not slow the aircraft. With thrust unchanged and the flight path inclined downward, the aircraft accelerates. A decreasing speed combined with an increasing sink rate would be typical of a nose up input followed by a stall or of an aircraft losing energy, not of a forward stick input.

The speed increases and the sink rate decreases → INCORRECT. A reduction of sink rate would require the flight path to become less steep or to become a climb, which is the opposite of what a forward stick input produces. Pushing the nose down steepens the descent, so the sink rate must increase, not decrease.

The speed decreases and the sink rate decreases → INCORRECT. This combination would correspond to an aircraft raising its nose and levelling off or climbing (shallower descent) while losing energy, which is inconsistent with a forward stick input. A nose down input does not produce a reduction in speed, and it does not flatten the flight path.