Is this mention of the double-slit phenomenon broadly correct? I'm reading a book of philosophy (Less Than Nothing by Slavoj Žižek) and a chapter in it (called The Ontology of Quantum Mechanics) frequently references the double-slit phenomenon. At one point it says the following three points:

(1) Even if we shoot the electrons individually, one after the other,
  they will, if we do not measure their path, form a wave pattern―but
  how can they? With what does each individual electron interact? (With
  itself.)
(2) Even if we measure (or not) the path after the electrons have
  already passed through the slits, the pattern still depends on our
  measurement―but how can it, when the measurement takes place after the
  passage through the slit? It seems as though we can retroactively
  change the past.
(3) Even if we do not enact measurement at all, the mere fact that the
  measurement apparatus (and, with it, the possibility of measurement)
  is there makes the electron behave as a particle―but how can it, when
  it was in no way affected by the measurement apparatus?

While I'm studying biophysics and I've done a course on elementary atomic physics and QM, I'm far from being qualified to tell whether these claims are problematic or not, and if they are indeed problematic, in what ways. Of course I'm not looking for an in-depth analysis, I'd just be glad if someone pointed out if there are fundamental and obvious misunderstandings contained in the quoted passage.
I'm especially suspicious about the third point - from my studies I would think that the mere presence of a measuring apparatus is irrelevant, what matters is the physical act of measurement and the perturbations it involve.
 A: This is an answer by an experimental physicist. 
Quantum mechanics started with the wave equation of Schrodinger and then the relativistic covariant ones of Dirac and Klein-Gordon. These describe single particles in potential wells and the solutions are called wave functions and their complex conjugate square gives the probability of observation/interaction/decay for given boundary conditions. This is the basic quantum mechanical framework, usually called first quantization. In this framework electrons, atoms   and molecules are quantum mechanical entities, described by the wavefunction. When measured they have particle type properties, i.e. an individual (x,y,z,t) location . Collectively they display  the wave nature of the wavefunction.
Lets take the statements one at a time:

(1) Even if we shoot the electrons individually, one after the other, they will, if we do not measure their path, form a wave pattern―but how can they? With what does each individual electron interact? (With itself.)

The electron does not interact with itself, it is described by the boundary conditions set up by the slit which will define the wavefunction and thus the  probability wave  that describes its behavior. Here is a single electron at a time:


Electron buildup over time

Each individual electron ends up as a spot on the screen, in its particle like aspect. The accumulation of electrons with the same slits ( boundary conditions) shows the probability distributions which has a wave pattern.

(2) Even if we measure (or not) the path after the electrons have already passed through the slits, the pattern still depends on our measurement―but how can it, when the measurement takes place after the passage through the slit? It seems as though we can retroactively change the past.

This is confusing . The screen can be up to the slits , the screen is a measurement and the pattern's widths will depend on the location of the screen , not the interference pattern which will be there. Only if a measurement apparatus is placed at the slits or on the way it will change the boundary conditions and thus the solution, and the pattern will be destroyed ( see 3).

(3) Even if we do not enact measurement at all, the mere fact that the measurement apparatus (and, with it, the possibility of measurement) is there makes the electron behave as a particle―but how can it, when it was in no way affected by the measurement apparatus?

This is confusing, it might be discussing a which slit passage detection. This by construction changes the boundary conditions of the problem . Changed boundary conditions will give different results and randomize the pattern. It is no longer the same problem. Also he is using "particle" pattern as classical, billiard ball particle which is not really true
This recent paper clears this type of confusion:

Overall, the results suggest that the type of scattering an electron undergoes determines the mark it leaves on the back wall, and that a detector at one of the slits can change the type of scattering. The physicists concluded that, while elastically scattered electrons can cause an interference pattern, the inelastically scattered electrons do not contribute to the interference process.

A: 
(1) Even if we shoot the electrons individually, one after the other, they will, if we do not measure their path, form a wave pattern―but how can they? With what does each individual electron interact? (With itself.)

The way to work out what's happening is to try to guess what's happening and then look for ways to rule out guesses. Suppose a single electron goes through just one slit and there's nothing else going on. At any given point on the screen, if you open up another slit, then that point should see more electrons because you've let in electrons that otherwise would not have come into the experiment. But you don't see that: rather, you can have fewer electrons at a particular point when the slit is open. So every time you detect an electron there was something going through both slits. If you put a detector in front of both slits, only one will go off at any given time, so the electron doesn't split into two parts, each of which goes through one slit. Nevertheless whatever is going through the slits behaves just like an electron: it can be deflected by magnets etc. So there are two versions of the same electron and they interfere with one another. See "The Fabric of Reality" by David Deutsch, Chapter 2 for a clearer explanation.

(2) Even if we measure (or not) the path after the electrons have already passed through the slits, the pattern still depends on our measurement―but how can it, when the measurement takes place after the passage through the slit? It seems as though we can retroactively change the past.
(3) Even if we do not enact measurement at all, the mere fact that the measurement apparatus (and, with it, the possibility of measurement) is there makes the electron behave as a particle―but how can it, when it was in no way affected by the measurement apparatus?

No. There are two versions of the electron, one going through each slit. Both versions contribute to the outcome of the experiment. Now, when the electron version going through the other slit comes to the place where you put the detector, it interacts with something that acts exactly like the detector. For example, if the detector blocked some particular subset of the electron's possible paths, that set would no longer contribute to the interference. But you don't see the detector go off, so there is another version of the detector that went off in response to the presence of the electron.
See
http://arxiv.org/abs/hep-th/9305002.
