What is an EM wave? 
*

*How does an EM wave carry energy? 

*What is an EM wave? (Is it a collection of photons?) 

*What are the mechanics behind it?
I am an engineer and I've been taught to think of light (light is my area of expertise, by the way) as an EM wave and what that means is I have been told that it carries energy via "oscillations" (which are more like a series of alternating fields coming one after another in a quick succession and the quicker is the succession in which the fields come the more energetic the wave is) and "amplitude" (which is the energy of fields per se) and that by changing the amplitude you can change the intensity of a light-wave. I was also taught that photons are energy carriers in light-waves. Well, does any of this make any sense to any of you here?   
 A: This wiki article has relevant material.

1)    How does an EM wave carry energy?

The EM wave is an ensemble of photons, so the photons are carrying the energy ( see answer to 3) . In the classical electrodynamics formulation of Maxwells equations it is the electric and magnetic field propagating in space that is carrying the energy.

2)    What is an EM wave? (Is it a collection of photons?)

An electromagnetic wave is an ensemble of photons

3)    What are the mechanics behind it?

The underlying framework of all nature is quantum mechanical. Quantum mechanics has equations whose solutions predict probabilities of interactions taking place, and not trajectories as is the case in classical mechanics and electrodynamics.
From this quantum mechanical underlying level of nature classical mechanics and classical electrodynamics emerges smoothly mathematically, although not simply.  The quantum mechanical equation that predicts the behavior of photons is a version of Maxwell's equation where the derivatives have become operators. Thus the wavefunction ( probability of location of the photon is the square of this) carries not only energy information which will build up the amplitude of the emergent classical wave, but also phases that will built up the phases of the emergent classical wave. 
If one reduces the amplitude of an electromagnetic wave to one photon at a time one can measure the energy of the single photon, h*nu . The behavior of the ensemble of photons will build up the classical E and B fields  with their energy and phases as predicted by Maxwell's classical equations. (an analogue in classical physics is how thermodynamics emerges from statistical mechanics)
This article may help, also this previous answer of mine.
A: Classical waves through empty space is the easiest.
There is actually energy at every place where there is an electric and/or magnetic field.  The amount of energy per unit volume is $\epsilon_0E^2/2$ for energy stored in the electric field and $B^2/2\mu_0$ for energy stored in the magnetic field.
So when the amplitude is larger both the electric and the magnetic fields are larger and so there is more energy stored in every bit of volume that has energy which is everywhere the fields aren't zero, which is almost everywhere.
As the wave translates across space in the direction it travels the regions of higher energy slide into a new location, much like a baseball player sliding in a base. This transports the energy from where it used to be into a new location, the location where the field is now large (instead of the location where the field used to be large).
What about all this talk about frequency? That has nothing to do with the energy stored in a given volume.
Quantum mechanically energy is transfered from the collective field to an object in discrete multiples of $\hbar\omega.$  Since a larger amplitude means more energy that means more multiples of $\hbar\omega$ can be delivered. And if the frequency is higher then each little bit of $\hbar\omega$ packs more punch. For quantum mechanics you also have to take into account the quantum nature of the thing getting the energy.
Quantum mechanically it is harder to say anything, even energy, is located somewhere. You can only talk about the dynamics of interactions. It is more complicated by the fact that there isn't really a classical electric or magnetic field in quantum mechanics.
A: The main point is the understanding how light or more generally electromagnetic radiation is emitted. Electrons, loosing energy, emit photons. Protons and neutrons can do this too. Switching on an electric bulb, in a current carrying wire electrons gain kinetic energy and loose a lot of this energy by getting negatively accelerated (braked) by the atomistic structure of the wire. The emission of photons is the only way the generate EM radiation.
Now, what are radio waves? To produce them one has to let through an antenna rod an alternating current. The generator do this, he accelerate the electrons in the wire periodically. It was explored, that accelerated electrons produce a magnetic field. And that a changing magnetic field produce a changing electric field. Each of the photons, emitted in aligned direction by the accelerated electrons in the antenna rod are oscillations of an electric and an magnetic field.
From the oscillation of radio waves one can conclude about the behavior of single photons. Photons are propagating in space by converting electric in magnetic field and magnetic in electric field and so on. More explanations in my elaborations here.
