So there is no wave particle duality.
By particle we tend to use the classical macroscopic definition of a particle, which means a shape( a volume) a center of mass that describes absolutely the particle's position in (x,y,z,t). A billiard ball, for example.
Electron is always a particle. But the location of electron is represented as wave, because of uncertainty principle.
The electron is an elementary particle , a basic building block of macroscopic matter as we know it.
A single electron in an observation, as in this single electron double slit experiment,
Electron buildup over time
is a dot in the picture. Thus each electron as it passes the slits ends up as one dot on the screen, of dimensions about a micron, having a specific ( x,y,z) , thus similar to a classical particle.
BUT as the electrons accumulate we see an interference pattern similar to the classical wave mechanics. The distribution though is of a population of electrons, not the same electron, and it gives a probability distribution that can be used to give the probability of finding the next electron at a specific (x,y).
Probability distributions have the same meaning both in the classical and quantum mechanical case. One cannot nail down a prediction, in a similar way that there exists a probability curve for life expectancy, given one's age, but it is not a prediction of death, except if one is 103 where the probability goes to .999999 ( a distant cousin of mine died at 103 the other day).
So electron can't interfere with itself because it is always a particle.
The electron is a quantum mechanical entity, described by a wave function and quantum numbers.
The interference is about its location function.
For a single electron given an ( x,y,z,t) there exists a probability it will be found if an experiment is carried out at that point in space time. Probability distributions can be seen experimentally by repeating the experiment with different electrons, not the same one.
1-) Are these all true?
In the qualified way described above.
2-) If true, if an electron is always a particle, in double slit experiment how does an electron interfere with itself without observer, but there is no interference pattern with observer?
You are talking of checking which slit the electrons go through as they pass. When one puts detectors at the slit , it is a different experiment, different wave functions.
The wavefunction of an electron going through two slits is one type of problem, a solution of the quantum mechanical equation with electron+two slits as boundary conditions. Putting detectors at the slits changes the boundary conditions. If grossly enough the interference is lost because the wavefunction is different. There have been experiments with minimal detection at the slit which clarify this: the greater the effect of detection the smaller the interference pattern.
We have realized a which-way experiment closely resembling the original Feynman’s proposal exploiting focused ion beammilling to prepare two nanoslits and electron beam induced deposition to grow, selectively over one of them, electron transparent layers of low atomic number amorphous material to realize a which-way detector for high energy electrons. By carrying out the experiment in an electron microscope equipped with an energy filter, we show that the inelastic scattering of electron transmitted through amorphous layers of different thicknesses provides the control of the dissipative interaction process responsible for the localization phenomena which cancels out the interference effects.