Can only one electron or photon produce interference pattern? If we shoot one electron or photon at a time to a double slit for a long time, interference pattern will build up on the other side. If the gap between each electron or photon is long enough that they don't interfere it appears that a single electron or photon is interfering with itself. So, is the interference pattern obtained by shooting only one electron or photon its just that we can't see the pattern because its too dim and so we have to shoot many electrons or photons one after the other to make the pattern brighter?
 A: You can't predict where the electron will hit, but you can measure that it will hit at some discrete point. The probability distribution of final positions on the detector corresponds to the interference pattern. 
You will see the pattern only after shooting many electrons:
https://physicsforme.files.wordpress.com/2012/04/slit.jpg
A: Short answer: no.  The interference pattern is formed only after many electrons are shot through the slits.  The "natural" conclusion of this experiment is that we cannot predict where an electron will be detected, only the probability of the electron being detected in particular locations, as indicated by the interference pattern.  Another remarkable aspect of this outcome is that it is indicative of wave-particle duality.  The single point of detection when shooting a single electron suggests particle-like properties, whereas the interference pattern suggests wave-like properties.
https://www.youtube.com/watch?v=MbLzh1Y9POQ (an excellent real-life video showing the build-up of the interference pattern)
A: The electron is an elementary particle.
Elementary particles are point particles - they have no extent. This is a basic postulate in the Standard Model of particle physics that has been tested over and over again the past fifty years.
When experimenting with elementary particles, we have to use quantum mechanics. It is proven beyond doubt that classical physics and classical concepts are unable to explain the experimental behavior of elementary particles and composites in dimensions commensurate to $\hbar$ of the Heisenberg uncertainty principle.
In quantum mechanics, predictions about the behavior of particles are made by solving boundary value problems with the quantum mechanical equations, but the solutions are not trajectories. The solutions describe the probability of finding an elementary particle at a specific (x,y,z) for the given boundary conditions. Because solutions of the QM equations are sinusoidal, the probability has a wave nature and can display interference patterns, as seen in the single electron two slit experiment. The accumulation of electrons on the screen reflects the probability distribution of an electron impinging on the boundaries of two slits to be found at each (x,y) of the screen.
In contrast to water waves, which are built up by energy transfers on the molecules of the water, the energy of the electron is localized at a point. The location of that point cannot be calculated in advance by using the only tools we have to study elementary particles - quantum mechanics. Only the probability of the electron's existence at that point can be calculated.
A: If you shoot only one photon, you will get only one "spot" (pixel, if your detector is digital).  One "spot" does not a pattern make.  However, you can predict that there are regions on your detector where the photon will not hit, and no "spot" will appear.
So there is a sense in which the rather poorly defined phrase "a photon interferes with itself" can be understood.
A: It seems to me that if shooting one electron does not produce an interference pattern that the conclusion that an electron is spread out everywhere and can be two places at once is wrong. It is also wrong to say that this pattern can only happen after shooting millions of electrons. Shooting million of electrons does not predict the behavior of one electron. It predicts the behavior of millions of electrons.
That's like saying that if you switch the electron with many baseballs and perform the same experiment, that because there is a pattern of two marks, that the position of the baseball is spread out everywhere and it can be at two places at once.
