I just tested with the current Preview build and changing that orientation setting works. Please try again with the latest Slicer and confirm that you haven’t made any other changes after a fresh start (i.e. the view can be rotated manually so to generate the view in your screenshot even if the “right is on the right” default setting has been selected).
Regarding the segmentation, probably unrelated to the view question. Depending on who generated the file and what format they used there can be many sources of error. We often see this kind of issue in nifti files generated by research software, so you need trace through the steps and see what conventions have been used. (see https://slicer.readthedocs.io/en/latest/user_guide/coordinate_systems.html