How [is] electrical energy is transfered [through] a wire
It isn't really, the energy comes in front the side and the charge flows through it and the two are different. Let's talk about the energy.
Firstly, the electrons fields and magnetic fields themselves have energy.
Secondly, when you charged up the battery you changed the electric and magnetic fields and put energy into them.
Thirdly when you started hooking up wires to the battery you changed the electric and magnetic fields and their energy.
Sure, all these changes get spread out through space and propagate at the spread of light, but what happens is that energy is exchanged from charges to fields and now the fields have that energy and all the speed of light stuff is just the fields moving the energy from one part of empty space to another part of empty space.
When you have a field and a charge in the same place they can exchange energy with each other.
So when you have a battery, you could either do some work to move charges in a way that makes the charge give some energy to the fields now (and then move it around). Or else you can get the charges ready to move and have something that can make them move in a way that transfers energy to the fields when you want it to. That is in general the two approaches.
As for where the energy is transported compared to where the charges are transported this depends on how good your wires are.
The current tells you how much charge is moving, and you could have the charges move quite slowly and have a big current if many charges move. And the fields could change in a different way or not at all.
See, fields exist everywhere in space, they don't move. They have a value at each point and the values at each point can change over time and that affects how much energy is stored by the fields in a region.
So indeed the energy can flow. But just like the current you could have a large flow of energy through a region that doesn't have much energy. Its like a line of people that only have a dollar, they could all reach out to give a dollar to the person on the right while taking a dollar from the person on the left.
It might look like the dollar you handed to the person on the farther left went to the person on the farthest right and did so rather quickly but it didn't. But if the line was a galaxy long and they took a second to grab and give then it might look light you sent a dollar across a whole galaxy in one second. You didn't really, your dollar only went to the person next to you there was just a flux of money. And so you might be able to send a dollar a second for an an hour and it looks like $3600 dollars were transmitted, but everyone only had a dollar. The flux (rate of transfer) and the density (amount in a region of space) are pretty unrelated (though not totally unrelated).
The flux of energy come in orthogonal to the electric field, so that means when you speed up and the electric field is increasing the z component of your momentum, the energy comes in from the direction of the xy plane.
So literally if there is an electric field along the wire then the energy (from the fields) is flowing into the wire from the outside.
So the charges have energy but when they speed up to get more energy, they get that energy from the sideways directions of where they are speeding up. And that energy they get, they get from the fields next to them, but the fields get energy from the fields next to them and so on, so the ultimate source could be quite far away. But there is energy distributed all throughout the region in between.
A simple example of a capacitor discharging has energy stored in the large fields between the plates and it flows sideways out of the capacitor, also flows sideways to the electric field at every point in between the plates and the edges of the wires and flows into the wires from the edges. It gives it to the charges, and the charges will either speed up, or if they are also bring slowed down by other things (e.g. a resistor) they will get energy from the fields and also give away energy to other things, for example by bumping into them.
Since you said you read the site, let's quote some relevant passages (with emphasis added).
Generators don't produce "electricity", they produce the electric pumping force. They also send out "electrical energy" which is made of invisible fields resembling radio waves that whiz along outside of the wires. Generators are charge pumps. They force the charges found inside the wires to flow along.
Batteries don't supply "electricity", the wires do. A battery is a chemically-fueled charge pump. Like any other pump, a battery takes charges in through one connection and spits them out through the other. A battery is not a source of the "stuff" being pumped. When a battery runs down, it's because its chemical fuel is exhausted, not because any charges have been lost. (Remember that a battery is just a Fuel Cell, but it keeps its chemical fuel on board.) When you "recharge" a battery, you are forcing charges through it backwards, which reverses the chemical reactions and converts the waste products back again into chemical fuel.
Light bulbs don't consume "electricity." Instead, the charges of the thin filament all flow along much faster than they would in thicker wires, and this heats the filament because of a sort of "electrical friction". Charges are forced into the bulb through one terminal, but then they all flow back out again through the other terminal. The quantity of charges inside the filament doesn't change, and none are used up.
Now let's talk about charge. The wires allow charges to move and they can enter one side and come out the other side. Much like water can move through a pipe. New water comes in, old eater comes out. You could have a treadmill that gets pushed by the water, slowing it down, and in other places you could have someone drive a treadmill to force water to go faster.
The treadmill and the eater can go at different speeds. And in the case of the fields the fields don't move. They have a magnitude and the magnitude can influence the speed at which the charges go. So more fields outside the wire can be coincident with more current.
Which means more charges moving slowly or a smaller number moving faster. And that faster motion could mean more energy lost to heating.
How does one electron interact with the other to push this energy foward?
The energy is flowing sidewise to the electric fields and in general the motion of the charges has an average motion in the direction of the field (because friction tends to destroy any net motion in other directions). So they are almost always giving energy to the fields in the sideways direction to the direction they are going (when they slow down) and and getting it from the the sidewise direction they are going (when they speed up).
When they are going at a constant speed it is usually because they are doing a bit of heating and getting an equal amount of energy from the sidewise direction. Not much heating means not much energy flowing so the flow of energy is actually quite small in many places.
So its a balancing that goes on.
When you go too fast you rush up on the charges in front of you and now they and you have to share the energy that us flowing in sidewise, so less energy for you and you still lose energy to heating so you slow down.
When you go too fast you leave the charges behind and now they don't have to share the energy that was flowing in sidewise, so more energy for them and so they catch up.
Just imagine there are some jobs giving money from the side. If they pay you more you can go faster when you go the same speed as everyone else it all works out. When you rush ahead you have to share the incoming dollars with more charges so can't go as fast. When those in front rush ahead there are more dollars for you so you can rush ahead too.
So everyone rushes ahead until it doesn't pay to do so. And the people behind catch up until the same happens to them. The balancing happens quickly. Eventually everyone is getting enough to pay the cost in friction based on the speed they are going at that region. The charges could still speed up or slow down as it goes around the wire but there develops a steady speed a speed for each section of wire where the balance between energy coming in as payment from the fields is exactly equal to what you need to pay in friction with a balance exactly needed to be going at the right speed in the next section.
I've seen no mentions about this,
The dynamics of getting to that balancing distribution is fast and often unimportant. And the final configuration just has a current (flow of charge) at each point and a flow of energy (coming in and out from that sides) that is just a balance.
For example: one electron is pushed foward, which repels other electron, and so on, the wave is transfered. Is it what happens?
Not really. The charges move and the new location takes energy away based on how much friction you need to move through it and supplies some energy from what is flowing in sidewise and that net energy changes the speed of the charge and usually that balances out to a magic speed at each place that involves an equal amount of charge coming into each region as leaves.
Before it reaches that perfect balancing speed at each point you might have different things going on. But the energy still comes in from a direction sideways to the direction you speed up.
When this wave hits a light bulb in the circuit, for example, it makes its electrons collide with each other, producing heat and light.
There is always some friction. What happens is at first the current might be quite small as you are starting to hook up the battery, but as the current starts to increase as you fully hook up the wire the flow requires more energy to be supplied to the region with the high friction. Charges are pushed in one side and pulled put the other and because of the high friction in the region lots of energy has to be supplied in that region compared to other regions. So the fields outside the wires arrange themselves so that more energy is sent through the regions outside the wires to land in that part of the circuit. Only then can each part send out as much charge as it gets coming in and get coning in what it is sending out.
Going back to the money example, it is like paying more in a region with a higher cost of living, people are not going to move from one region to another with out. And since the energy comes from the sideways direction the fields outside the wires have to change. Since the energy flows into the wire there the field points along it and that's why we say there is a voltage difference long that section of wire.
More energy needed means stronger fields are needed so a bigger voltage change across that part.
But the article says that charge still continues in the circuit.
The charge flows in and because it looses energy to friction it needs energy from that fields to come in from the sides to keep moving at the same speed and needs even more if it had to speed up for the next section (though not as much if it needs to go slower in the next section).
If you prefer a car example, imagine cars with super small gas tanks, they have to get gas all the time, so stations supply fuel all the time, and in regions where they go up steeper hills they need more gas stations which is bigger fields so bigger voltage changes.
The big problem is that it says charge is a property of the matter, like mass. So how can it be transfered through the circuit?
Each piece of the wire has some charge. Some parts stay still. Other parts move. The parts that move might have lots that move slow or a smaller number that go faster. and they experience friction. Each part has a numerical charge and an equally charged amount needs to come in as leave for the balancing distribution to be achieved.
How can you transfer a property, like mass, for example?
If you thew a baseball at me, you would transfer mass. If you took a charged part of the baseball off of it and three the rest at me, you'd transfer charge and mass. But if I did the exact same thing to the person next to me, then neither my mass nor my charge would increase, I'd have the part I kept and the baseball you sent which is missing that same part so I would have all the parts to a baseball.
What's really a transfer of charge?
I need to understand what's flow of charge because that's how current is defined.
Each electron has a charge if each section sends some old electrons one way and gets an equal number of other new electrons from the other direction then charges flowed even though the amount of total charge in each region didn't change.
For other situations the flow could be protons (which also have charge) like in some batteries or ions (like in many fluids).