I'm not sure what you mean by "New" HSC Math courses (you mean progressing to senior or a complete revamp in the content?)
Anyhow, all I can say is that you general math is basically learning applied "real life" math like finding areas and doing some basic finance stuff you might encounter in everyday life.
The difference between Math advanced and the Extensions is that Extensions build up on from Advanced in addition to some new concepts, and naturally at a much higher level. So taking Extension 1 for example would mean that you also have to take Advanced in conjunction, taking Extension 2 would mean you have to take Advanced and Extension 1 in conjunction, BUT you won't need to take general math as that is a different course in it self that doesn't get applied to the aforementioned courses.
You don't need to do general maths if you take Maths Advanced, Extension 1, or Extension 2.
In the new syllabus, Maths Advanced is worth 2 units, and Extension 1 and 2 are each worth 1 unit. As a result, you will still need to do Maths Advanced even if you take Ext 1 or Ext 2.
Not entirely true, if you take up Extension 2, then Advanced is worth nothing, and Extension 1 and 2 are worth 2 units each.