How could electromagnetic waves propagate through space although they have no electrons? How could electric fields in these waves propagate through space although in space there's no electrons for the electric field to be formed? is there another type of charged particles that carry the electric field?
How could the electric field exist without charges?
 A: This is a question that was drastically changed and the other answer and the comments to the question and the answer are discordant with the edited question.
I already advised in the comment that you read a simplified article in wikipedia on electromagnetic radiation. Classical electromagnetic radiation cannot be simplified easily by analogies. I will try to explain with the quantum mechanical framework which is the underlying framework for all physics, classical theories emerge from this framework smoothly.
The electromagnetic wave is composed by a huge number of photons. Photons are elementary particles, they have zero mass, are point particles and their energy is characterized by the frequency of the classical wave we observe macroscopically, given by 

In addition photons obey the Maxwell Electromagnetic equations in their quantum mechanical form. This means except their spin and energy they are characterized also by the vector potential entering the Maxwell equations. 
You must have no problem accepting how a single photon can travel in space, even in vacuum. It is a quantum mechanical particle which will go in a straight line if it finds nothing to interact with. Single photons have been measured by making laser beams very faint so that only one hit happens on the detector at a time. They even have commercial single photon detectors.
The question goes into how zillions of photons  can build up the electromagnetic waves that come to us from the stars, for example. They add up in a similar way that water molecules add up and make up streams, except in smaller dimensions and faster times. A stream of photons arrives continuously from those stars with the impetus given when they left so long ago. 
If the light is coherent, i.e. the disparate constants describing each photon mathematically have a fixed phase , the individual fields, E and B  described  macroscopically with a wave equation, can be seen schematically:


This 3D diagram shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together

The wave is built up by zillions of photons in step so that their spins, and other constants describing them build up the macroscopic wave, even though it is made up of all these elementary particles, all going in a straight line unless they hit something on the way.
A: (I am refering only to the updated question)
This is a question which has been asked numerous times by physicists after the formulation and popularization of Maxwell's equations. They have previously known the wave equations on strings where the matter of the string was vibrating, or on water, where the water surface was the one carrying the wave. 
How could it then be that a wave is "happening" around us without any kind of matter carrying it? To sate the need of visualization, a certain fabric pervading all space, even the vacuum, was postulated, the aether, which carried the electromagnetic wave. This concept was so popular, it was even used to describe curious transformation properties of the electromagnetic field. However, Poincaré and Einstein later showed that the aether is redundant in the latter sense and that we were actually just using the wrong transformation the whole time (yes, relativity was born).
Nowadays we just say the electromagnetic wave is carried by the field itself. The ripples in the field just propagate on their own even in vacuum. Actually, the waves propagate the best in vacuum and things such as electrons are obstacles for them! This is just a concept you should become comfortable with before proceeding to the next paragraph.
The last insight we can get is when considering the quantum nature which applies to every field. From a rather complicated argument it follows that field quanta are actually particles flying through space. A particle, even though massless as is the case of a photon, can be really easily understood to fly through space without any kind of "support".
As for the question of creation of electromagnetic waves, there indeed isn't a way of producing an electromagnetic wave without charges. However once produced, the wave flies around freely. In certain idealized situations, we can concentrate on the wave itself and put the sources "very far" producing abstractions such as planar waves which is probably the example which motivated your question. 
Planar and other idealized sourceless waves are just an approximation to the case where the producing charges are very far away, so we can work with a simple asymptotic form of the waves.
A: Air resistance acts only on macroscopic objects travelling through air. Electric fields are not affected by this at all. Electromagnetic waves do not even require a medium to propagate, so there is no point in even discussing how they can propagate through air. I think you are confusing Permittivity of air with air resistance, as anna mentioned in the comments.
