Refer to figures.
The pendulous magnet inside the direct reading magnetic compass will align itself with the magnetic flux lines of the Earth’s magnetic field. But these magnetic lines are not straight lines spread equally around the Earth. They’re straight and horizontal close to the Equator, but the higher the latitude, the more these lines tend to converge towards the Earth’s poles. Therefore, they will become more and more inclined until being fully vertical at the pole. As a consequence, the pendulous magnet will also increasingly tilt towards its vertical, as the compass approaches the pole.

Magnetic Dip is the tendency of a magnet to align with the Earth's magnetic field lines, causing the north end of a compass needle to dip down in the Northern Hemisphere (positive dip) and up in the Southern Hemisphere (negative dip). The magnetic compass will tend to dip more at the poles than closer to the magnetic equator.

“Only when turning through northerly and southerly heading.” → CORRECT. Turning errors are greater on North/South headings and at high latitudes as they are directly related to the vertical component of the magnetic field of the Earth. The higher the dip angle induced by the vertical component (so at high latitudes), the larger the turning errors.

• When turning from a North heading, the compass initially lags behind or even moves in the opposite direction. 
• When turning from a South heading, the compass leads the turn, showing a greater amount of turn than has actually occurred.

In the Southern hemisphere, Pilots use the mnemonic ONUS:

• Overshoot North: The compass leads when turning toward North.
• Undershoot South: The compass lags when turning toward South.

“When turning though all heading” → INCORRECT. While magnetic dip exists everywhere except the equator, the mechanical configuration of the compass pivot and weights eliminates this specific "turning error" when the aircraft is passing through East or West headings.

“Only when turning though easterly and westerly heading.” → INCORRECT. Turning errors do not occur when turning through these headings because the magnet's center of gravity and its pivot point remain in alignment relative to the turn.

“When accelerating on easterly or westerly heading.” → INCORRECT. When accelerating on easterly or westerly heading: While this is a real phenomenon known as acceleration error (remembered by the mnemonic ANDS: Accelerate North, Decelerate South), it is distinct from turning error, which is specifically caused by the banking of the aircraft during a change in direction.