As far as I know Mendix uses Java SimpleDateFormat to format and parse dates - https://docs.oracle.com/javase/7/docs/api/java/text/SimpleDateFormat.html
Perhaps you can find answers by searching for your problem on StackOverflow or other non-mendix specific forums.
Hope this helps,
As Andrej said, Mendix does use Java formats for date time.
I took your last example and tested them out in 7.6. In addition, in case the embedded T was causing some issues, I tried a variant that isolates the T as a separate string. The results are shown below from a message box:
Is this what you need to end up with? If so, I am not sure why your example yields the result that it does. Anyway, maybe breaking it up a bit will help you troubleshoot what's happening.
I found the problem. The modeler (actually the debugger) is confusing me here. I tried with this:
The debugger shows me this:
But then when I look at the Soap XML that was generated ( I'm calling a microflow in the mapping):
And this what I want :)