This is no code question.
Does using an Arduino mean, we are all set and you just use an already existing lib and put the code together? I do not think so and therefore want to apply my c-programming skills and manipulate registers, as learned in school.
There are three obvious programming ports on the Arduino Due: - usb prog - usb native - jtag
Do I need the Arduino Application to getting started? (reason?) Which other programming tools are available, instead?
I was thinking about using the controllers manual and a simple programming environment + jtag. http://www.atmel.com/devices/sam3x8e.aspx
Sorry for asking, but is there a description for doing that? (Yes, I want to learn further more about micro controllers. It does not mean I want to reinvent the wheel.)
Arduino IDE isn't the only option to write programs for Arduino DUE. As one of the options you can use arm-none-eabi toolchain to build binaries from your code and bossac command line tool (or bossa GUI tool) to upload your binaries to Arduino DUE. You can find both in Arduino DUE package for Arduino IDE or download them separately.
I would recommend this article: "Low level" programming of the Arduino DUE SAM3 controller with a custom IDE . I also found this "ARM skeleton" GitHub project very helpful (you can use it as starting point for your Arduino DUE program in C).