1. I would like to know how to change an object's origin so that its' (0,0,0) is also the document's - world's(?) - (0,0,0). (Hope the picture explains my non native English...)
It's up to you to define the object's origin. Then to move this point to the origin in world coordinates just set the Position attribute of the Placement to the negative origin of the object.
2. Also I am really having problems in understanding rotation in detail. When I import a curve I always see it in top view. To see the same in right view I would have to rotate 90° around the x axis and then 90° around the z. I somehow understand why it is not working by just setting axis to 90 and x AND z to "1", but not how to achieve what I want.
If you only want to *view* the object from another perspective then you shouldn't rotate the object but rather the camera of the 3d view.
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Gui.activeDocument().activeView().viewRight()
If you insist on rotating the object you have to write:
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from FreeCAD import Base
App.ActiveDocument.ActiveObject.Placement.Rotation=Base.Rotation(-0.5,-0.5,-0.5,0.5)
3. Can I rotate an object around one of its' edges? Or any edge in the document?
Yes, that's possible. The edge gives you the rotation axis, one of its endpoints gives you the rotation center and the angle is freely selectable. The idea is to first move to the rotation center, then do the rotation and afterwards move back.
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s=Gui.Selection.getSelectionEx()[0] # get the selected object
e=s.SubObjects[0] # get the selected sub-object, i.e the edge
p=e.Curve.StartPoint
q=e.Curve.EndPoint
axis=q-p
t1=Base.Placement() # the movement to the center
t1.Base=Base.Vector(-p.x,-p.y,-p.z)
t2=Base.Placement()
t2.Rotation=Base.Rotation(axis, 25) # the rotation around the edge by e.g. 25 deg
t3=Base.Placement() # the movement back
t3.Base=p
# multiply all three operations to have one
t=t2.multiply(t1)
t=t3.multiply(t)
# now apply the placement
App.ActiveDocument.ActiveObject.Placement=t
