Question: Is it possible to simulate user input? And how can I realize this?

I need to automate user interaction with an windows application. The problem is, that this application doesn't provide an API for one special function I need to call. But this function is accessible in the application window by standard mouse input.

I am not tied to any programming language. I only need to write an application which does the same, like I do with my computer mouse input.

Answer: 
I haven't used it myself, but [AutoIt](http://www.autoitscript.com/site/autoit/) seems to be what your looking for.
You could use Telerik Test Studio - <http://www.telerik.com/teststudio/>, Sikuli - <http://www.sikuli.org/>, Microsoft Visual Studio and UI Automation - <http://msdn.microsoft.com/en-us/library/aa348551(v=vs.110).aspx>, or AutoIt - <http://www.autoitscript.com/site/autoit/>

Telerik Test studio provides very decent recorder which will allow you to record your test without writing any code.