Controlling distance I want to move a copy of the right edge of the surface along its top edge for a certain distance (marked with red arrows on the screenshot). To do this, I turn on snapping to edges, select the right edge, press Shift + D, move the cursor along the top edge, but there is no possibility to enter the desired distance from the keyboard... In the lower left corner, coordinates in the global system are highlighted and i can enter them, but it doesn't help me. The difficulty is that neither the surface nor the edges are parallel to any coordinate axes. Does anybody has an idea how to do that, or how else this can be done?
ShiftD duplicating an edge will not cut an edge into the face. The duplicated edge will just hover there, unconnected to the rest of the object. Probably what you want is?...


Select the edge you want to slide along, and CtrlAltSpace create a Custom Orientation from it. (Check 'Use After Creation'). 
Create the edge you want to slide, in the face, any old how, eg.  K cut it with the Knife tool, not worrying about accuracy
GG slide it down all the way to the end of the face, where it will be stopped by the end vertices
GYYYour Number move the edge back again, to the required distance from the end, parallel to the orientation edge.


.. but this method will work just as well with a duplicated edge, if that's what you want.