How do Repetier coordinates setup work
I'm not sure exactly sure if you have one problem or two distinctive ones.  However a few notes:

The latest version of Slic3r PE can always be fetched on their GitHub release page.  At the time of writing that would be version 1.38.5, but I concur with you that that is unlikely to be the problem.

Mirrored objects are a clear indication that one of the Cartesian axis is swapped (not that it is translated).  Any of the axis can be swapped, but since the peculiarity of your printer is that the homing point is at the front RIGHT, I would guess the axis that got messed up is the X one.

I have no way to test the following, but if I got the meaning of your first two pictures, then I guess the correct settings in Repetier may probably be these:



If even that fail, check the handedness of the coordinate system of the software generating the model you are trying to slice.  Modelling software like Blender and others are typically right-handed, but many tools for processing those model for on-screen application (movies, videogames) are left-handed.  That means that even if the model display correctly in the native editor, it may be rendered mirrored in another software.