When I load a file to morph, I always hear the original recording as well as the morphed version. And the same when I actually perform the morph to a file, there's both voices. Is there a way to get only the morphed voice?

The Duplex should let you hear both the original voice and the morph
voice. So in this case, try to turn off the Duplex to fix this. If
you do not want to keep the source files after morphing, remember to
tick on "Delete sources files" on the top-left of Morpher module.