Please correct my understanding of "how electric works"
Well, electrons hop, but slowly.  

Let's get a bit deep in your questions: electricity flows in metals because their atom are bond by the metallic bond. That means that the nuclei are organized in a nice lattice, or at least they are still, while the electrons are free to move. Since we can't really nail down where an electron is we say that the probabilty of an electron being around a nucleus is the same for each nucleus.
When you have a single atom instead its electrons are well organized around it, and only it.

You can try to imagine that as a regular, 3-D grid where each node is a nucleus, and all the electrons are a sort of cloud.

Now, these little guys move very fast. Their speed increases with temperature, but here comes the trick: since they don't prefer a particular direction on average they do not move. And since current is defined as flow of charge per unit of time, well, there still is no current.

Imagine to cut a wire with a surface, and start counting the electrons that are going through it. There would be a lot of them going right to left... And vice versa. So the so called net charge flow is zero.

Now apply an electric field to the wire, i.e. connect it to a battery: the electrons now have a favourite direction, that is the lowest energy direction. Low energy for an electron (negative charge) means high electric potential, so the whole bunch of them starts to move towards the positive pole of your battery. Be careful, this does not mean that they stop moving randomly around, it just means that, on average, they are moving towards plus.

I don't really have an example for that, you know those seeds with a sort of wing on them, on a windy day they can fly for quite a distance: they move randomly but ultimately they follow the wind.

Now you have current: if you imagine to cut your wire again the electrons flow is not balanced any more. The so called drift speed of the electrons is very, very low, some mm per minute. So how is that you don't have to wait hours for your light to turn on? That's because all the electrons of the wire start moving simultaneously. The point is that when you apply an electric potential to a long wire, i.e. you close the switch, the potential is distributed along it. So for each tiny slice of wire you will have a potential difference, thus a drift speed, thus a current. This thing is almost istantaneous, and can be as fast as light (but it's slower).

Hope that's enough for your first question, now the others:

Electrons vs Electric Charge

Well electrons are physical objects, they have a mass, dimensions, and charge. Charge is a physical quantity. That's as you were asking the difference between a mountain and height: a mountain, among other characteristics, has a certain height that can be expressed in meters. An electron, among other characteristics, has a certain charge that can be expressed in coulombs.

Larger charge/voltage \$\rightarrow\$ faster electrons 

First of all charge and voltage are two completaly different things. The higher the voltage, that is the larger the electric potential, the larger the electron speed and then the larger the current. Larger charge means larger current if that charge is moving, if you just use a bigger wire that contains more electrons you will have a larger current only because the resistance of the wire is lower.