How can EM waves propagate indefinitely when they really are oscillations of electric and magnetic fields? I can't claim that I've fully grasped the science behind EM waves, but as far as I understand, EM wave is basically oscillations of electric and magnetic fields kinda switching back'n'forth and triggering each other in cycles.
Both electric and magnetic fields get weaker and weaker as you move away from the source. I don't see how switching them back'n'forth would change that.
And yet, EM waves can propagate indefinitely.
Could you explain how this works, please.
 A: 
basically oscillations of electric and magnetic fields kinda switching back'n'forth and triggering each other in cycles.

This is a misconception. Mathematically the electromagnetic wave can have synchronous electric and magnetic fields, the zero's and peaks in phase. 

Both electric and magnetic fields get weaker and weaker as you move away from the source.

This is about electric and magnetic fields from independent sources. The self propagating electromagnetic field (light) if in a plane wave can go on indefinitely. If coming from a point source , it disperses , the energy flow per unit area falling  with the inverse square law followed by  all point sources.   .
Here is an animation of an electromagnetic radiation:


Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation 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 plane wave above is a mathematical construct, approximately fitting radio waves, but not visible light which comes from point sources. 
Electromagnetic waves from a point source  will be loosing intensity by the $1/r^2$ rule . If very far away from the source both electric and magnetic fields whose amplitude give the energy per unit area will stop being measurable. BUT then there are the photons which may continue on until  they interact, as the classical wave emerges from a superposition of zillions of photons, but that is a different story. 
A: If you consider a static electric field, its energy falls off as $1/r^2$ as you move away from a point source, as $1/r$ as you move away from an infinite line source, and not at all as you move away from an infinite plane source.  However, there are no infinite line or plane sources so, at a great enough distance, field energy will fall off as $1/r^2$.  The fall off is the same for waves.  This is why the far away stars in the night sky are not as bright as the nearby sun.
However, the light from the stars is, in fact, reaching us.  The light will continue to propagate until something absorbs it.
A: Nobody fully grasps it but there are lots of features to appreciate.  If you want to get deeply into it you can google "photon wave function" to learn some of the subtleties. Some general items: 1) Radio waves, usually made from electric currents in antennas, drive zillions of photons into space and the the energy does indeed tend to fall of with distance.  2) An atom in a distant star can give off one photon and it will propagate forever(?) to the edge of the universe or come to excite the back of your eye, which direction the photon decides to emit in the first place is just probability or Quantum Mechanics. 3) Because light travels in a vacuum scientists say there must be an EM field that is capable of carrying the EM radiation, and this field is everywhere. 4) Feynman proposed that light likes to travel distances n multiples of its wavelength, this is why laser cavities have precise dimensions. 5) Interference and the double slit experiment can be explained classically (cancellation of energy) but a photon wave function explanation says there is no energy in the dark bands and all energy in the bright bands (energy is conserved), the latter is consistent with a photon travelling n times its wavelength. 6) Mach-Zender and Quantum Eraser experiments show unusual "photon" behaviour, the photon wave function helps to explain these.
A: Electric and magnetic fields do not lose energy. That is not why they get weaker with distance at all. 
They are becoming weaker , is equivalent to saying that a detector (designed to capture EM waves) gets only lesser individual signals (or if you think in terms of photons, there are only lesser number of photons striking the detector - just wrote this for clarity).
Why does it happen? It happens because the wave travels radially when they are emitted from a source - a point source in this case. If you keep increasing the distance between the detector and the source, there will be lesser number of photons striking the detector. I hope you get the idea.
Nothing affects the EM waves themselves (i.e. the electric and magnetic parts of the oscillations remain unaffected, unless of course they are tampered by noise).
This noise could be other EM waves as well. 
A: 
EM wave is basically oscillations of electric and magnetic fields

Let’s agree that if one can measure an oscillation, it’s some kind of wave. By measuring the light from a thermic source, be this an electric bulb in a DC circuit or the sun, you are not able to measure periodical changes in the intensity of the light.
Dimming this EM radiation to a very low intensity you observe that light consists of a stream of quanta (so firstly called by Einstein and later named photons).
The fact that this photons have an oscillating electric and magnetic field was established long before the technology of ultrashort laser pulses was used to measure these fields for single photons. Hertz measured the EM waves from a spark gap transmitter:


Electromagnetic waves are radiated by electric charges when they are accelerated. Radio waves ... can be generated by time-varying electric currents, consisting of electrons flowing through a conductor which suddenly change their velocity, thus accelerating.


From the behavior of the radio wave you may conclude about the behavior of each of the involved photons. With the knowledge about the emission of photons from accelerated electrons we know in our days that radio waves are an oscillating in intensity stream of polarized photons. Polarization means that the electric and magnetic field components are spatial and temporal aligned.

Both electric and magnetic fields get weaker and weaker as you move away from the source... Could you explain how this works, please.

The emitted photons are indivisible units between their emission and absorption. From a star like our sun, but very far away from us, you may get a stream of single arriving photons. The time between the arrival of these photons is random, you get a very week EM radiation from this star. From a very far away pulsar you may get also individual photons, but this time with a swelling number of photons in a time unit. A kind of wave.
