What azimuth description systems are in use?
There are many indeed. 

It may be specified from South westwards(0° to 360°), or from North eastwards and westwards(180° to -180°).

The most popular one, as used by Roy and Clarke in "Astronomy : Principles and Practices" is to measure the azimuth from North eastwards 0° to 360°. For a southern hemisphere observer, this system changes to from South eastwards 0° to 360°.

With so much confusion, how do professional astronomers go about it? They simply specify the system they are using in a given document. Doesn't cause much trouble since the differences in all of the systems is by an angle of 180° or 360°. It just causes sign changes in all formula.