Unfortunately I don't really understand what you're asking in (1), but for (2) you'll find a book list here: http://mathematica.stackexchange.com/q/18/12

Two freely available books are Mathematica programming: and advanced introduction by Leonid Shifrin and Power programming with Mathematica by David Wagner.  Both of these will teach you the fundamentals of the language, up to an advanced level, but they won't discuss domain specific functionality (such as image processing, etc.)  However, once you're comfortable with the base language itself, it's easy to use the documentation to look up specific functionality (that would be provided by libraries/packages in most other languages)

I have only a rudimentary knowledge of Geogebra, but I think you would find that anything you can do in Geogebra you can duplicate in Mathematica, but Mathematica is immensely more powerful.

In Mathematica you don't "create a 3D axis (itself a problematic idea) and a plane" as much as define geometric objects in relation to a coordinate system. All your geometric and display operations are carried out on that data set.

With Geogebra, as with other drag-n-drop programming systems, you can produce dazzling, expressive, illuminating results very quickly, but you're ultimately limited to the scope the package authors thought of.

It's going to be a universal problem, figuring out how to make the transition between the drag-n-drop sensibilities and the bits-n-bytes approach. Maybe, the drag-n-drop systems will advance to the point that they'll be capable of doing everything.

I think you must be on the leading edge of this, so you're going to have to tell us.

Hth,
Fred Klingener

for  ebook?is  there  any  ebook  from  official s ite  to  buy  it?