Is it normal or expected or unusual to take another type of examinations too?
In order to gain admission into an Australian university a student will only need an ATAR in most circumstances. This can be achieved by doing either the HSC or IB in NSW, but interstate and other international accreditations can also usually be converted to an ATAR.
However, some courses do require additional exams to be taken. Most notably undergraduate medicine and law schools typically require the UMAT and LAT respectively. The UMAT (undergraduate medical admissions test) is required by all undergraduate medical schools, but the LAT (law admissions test), which is still relatively new, is not yet required by all undergraduate law schools. Make sure to check with the specific institutions you may want to apply to.
If you are interested in applying overseas different countries may require additional exams to be taken. Most notably, the United States requires the SATs. Crimson offers expert consultations which will identify exactly which examinations you will need to take to apply to the university of your choice.