Is it possible to use the functions from ArcMap's main menu (for example Add Data, Start Editing) in my model? I can not find a way to add any other functions except Toolboxes.
There is actually one hacky method. To use COM objects in Python and in this way to communicate with ArcObjects.
There was already such topic here: How do I access ArcObjects from Python?.
Read also this presentation: Using ArcObjects in Python.
and this thread on Esri forum: ArcMap 10, ArcObjects, and Python: very cool, but help with a couple of problems?
ArcToolbox tools or standalone Python scripts are the only entry points available to ModelBuilder. Access to other tools or ArcObjects entry points are currently not supported.