Given more opportunities like this thread, Marlon and I might write identical posts, or, more likely, ones that say much the same thing.
Now, one of the reasons that QM is difficult to grasp -- weird, contradictory, "shut up and compute", "but we really don't understand it" -- is that the phenomena that led to QM are strange, weird -- blackbody radiation, photoelectric effect, atomic spectra, electron and neutron diffraction, pair production, spin, and on and on.
For the double slit business, first review basic probability, preferably discussed in terms of events. That will cure you of any concerns about predictions of single events. For all practical purposes, the theory of electromagnetic wave diffraction and electron diffraction are very similar -- the diffraction occurs primarily from restriction of the impinging wavefront, just like Huygens told us a few years back.
Interfere with itself? In my view, that's a personal choice. In fact, given the broader behavior of waves governed by Maxwell or Schrodinger, I see no good reason to formulate such a controversial notion. It only serves to muddy and confuse something that is basically straightforward, provided you accept that the phenomena of particle diffraction does occur . Then the point is to accept reality and figure out a theory that can explain how such diffraction occurs. QM does just that, and has done so for almost a century. Also, contrary to some contentions that have appeared in this forum, the vast majority of physicists accept QM -- albeit sometimes in different flavors.
As Dorothy said, "Toto, we're not in Kansas anymore."