<p>For a project of mine I would love to provide auto completion for a specific textarea.  Similar to how intellisense/omnicomplete works.  For that however I have to find out the absolute cursor position so that I know where the DIV should appear.</p>

<p>Turns out: that's (nearly I hope) impossible to achieve.  Does anyone has some neat ideas how to solve that problem?</p>

This
blog post seems to address your question, but unfortunately the author admits he has only tested it in IE 6.
The DOM in IE does not provide information regarding relative position in terms of characters; however, it does provide bounding and offset values for browser-rendered controls.  Thus, I used these values to determine the relative bounds of a character. Then, using the JavaScript TextRange, I created a mechanism for working with such measures to calculate the Line and Column position for fixed-width fonts within a given TextArea.
First, the relative bounds for the TextArea must be calculated based upon the size of the fixed-width font used.  To do this, the original value of the TextArea must be stored in a local JavaScript variable and clear the value.  Then, a TextRange is created to determine the Top and Left bounds of the TextArea.