When does the interference pattern of DSE disappear as size of "projectile" is increased? In trying to learn about Quantum mechanics (QM) from popular science books and Stack Exchange (I of course expect my knowledge to be anything but complete) I regularly come up with seemingly childish questions where I wish I could interrupt the author or visit them during office hours.
I'd prefer low level answers (beginning undergrad in maths with no formal physics whatsoever).
Regarding the double slit experiment (DSE):
Q1: I've heard about Feynman's view that the electron somehow takes every possible route from start to finish. For example, in Brian Greene's "The Elegant Universe" (TEU): "Feynman argued that in traveling from the source to a given point on the phosphorescent screen each individual electron actually traverses every possible trajectory simultaneously."
How can this argument be made without violating FTL?
Q2: When does the interference pattern result of DSE disappear as you increase the size of the "chunks" fired? E.g. if you fire protons or even larger ensambles. And, does it happen for all discovered particles? Is there a sharp point at when this happens or does rather the interference pattern disappear gradually?
 A: 
How can this argument be made without violating FTL?

By thinking about the electron as not being a  particle taking many separate classical  paths simultaneously, but instead as a probability distribution, spread out so that there is a distinct probability of finding  it any point along any path.

When does the interference pattern result of DSE disappear as you increase the size of the "chunks" fired?

The interference pattern occurs because the electrons have wavelike behavior, and the distance between slits (and slit width) should be similar to the wavelenght of the electrons.  Objects with mass, have a De Broglie wavelength given by $$\lambda=\frac{h}{p}$$ where $p$ is momentum and $h$ is Planck's constant. You can determine at what point the interference pattern disappears for increasing mass.

E.g. if you fire protons or even larger ensambles. And, does it happen for all discovered particles?

Yes. All particles have wavelengths, though the wave behavior and therefore interference pattern, will not form as their mass approaches that of classical objects. If you could increase the mass of the particles being fired,  the interference pattern will disappear gradually.
A: What Feynman is pointing out is actually a general wave property. For example, light passing through a slit can also be seen as a a superposition of all possible directions, note however, with an intensity equal to the slit's Fourier transform. At a distant, in terms of wavelength, point P all of these waves arrive, but only the wave with k-value pointing from the slit to P survives destructive interference. This is one of the fundaments of Fraunhofer approximation, the other being the assumption of small angular extension of the slit at P.
