Refer to figure.
Backing and veering are specific meteorological terms describing changes in wind direction over time at a fixed point, or with altitude. Backing refers to an anti-clockwise change in wind direction: for example a wind changing from south to south-east to east is backing. 

Veering refers to a clockwise change: for example south to south-west to west to north-west is veering. In South Africa, backing at the surface is associated with cold front passage (NW to SW is anti-clockwise = backing) and worsening weather. 

These definitions are internationally standardised and do not change between hemispheres: backing is always anti-clockwise and veering is always clockwise.

A wind that is changing in an anti-clockwise direction → CORRECT. Backing is by definition a wind direction change in the anti-clockwise sense when viewed from above, whether the change occurs over time or with increasing altitude. This is the standard and universally accepted definition.

A wind that is changing in a clockwise direction → INCORRECT. A clockwise change in wind direction is VEERING, not backing. These two terms are direct opposites and must not be confused.

An increase in wind speed over a short period → INCORRECT. A rapid increase in wind speed is described by terms such as squall or gust. Backing describes only the DIRECTION of change, not speed.

A decrease in wind speed as altitude increases → INCORRECT. This describes a negative wind shear or wind decay with height, which is a completely different concept unrelated to the directional meaning of backing.