Am I just some energy traveled at light speed? I don't understand $E=mc^2$ very well, and here is my question: 


*

*Does this equation mean masses are just condensed energy? 

*And does this mean that the extra energy an object has when traveling at light speed simply becomes mass? 

*So then are all masses just energy traveling at light speed? 

*If so, isn't light suppose to be relatively stationary for us? 
 A: I will try to answer this question with my basic understanding of special relativity:


*

*Is matter condensed energy? It kind of is, but a better way to phrase it would be that everything that has energy, (behaves like it) has mass. Imagine you have a hollow box with the insides covered with perfect mirrors and you put it on a scale. If you shone a light inside the box, it would contain photons which have energy and the scale would indicate that the box is heavier. Although the effect would be very, very small. Also light gets bent when it passes near heavy objects. It is important though that you distinguish rest mass and relativistic mass. As stated in the previous answer, $E=mc^2$ is just a special case of the more general $$E^2=(m_0c^2)^2+(pc)^2$$ with $m_0$ being 'rest mass'. Rest mass is the mass an object has when it is in rest, which is usually the same mass you read on your scale. Light has zero rest mass and all its energy comes from momentum ($p$). Relativistic mass is the mass that a particle appears to have due to its total energy: $$m_{rel}=\frac{E_{total}}{c^2}$$which explains why light gets bent near massive objects. You would still say that photons have no mass though.


*Objects with mass (read: rest mass) can't reach the speed of light. It follows from the relativistic mass that as something accelerates, its momentum increases and so do its energy and relativistic mass. Which means it becomes harder and harder to accelerate it any further ($a=\frac{F}{m_{rel}}$ still holds). So no it doesn't. Objects traveling at any other speed will have an increased relativistic mass though, but keep in mind that the effects are almost always so minuscule that you won't notice it in most cases.


I'm sorry to say this, but questions 3 & 4 don't make any sense to me, but I hope that my answer made some things clear to you.
A: Given the context of the question, the fact that it seems to be about $E=mc^2$ specifically, and that the OP says he's having a hard time understanding it, i'm going to try and give a simple answer in plain english without a load more complicated formulae.
I am no physicist, and although the concept may not be that easy, the formula is pretty simple, maybe even simpler when quoted (loosely) from einstein.

Energy ($E$) is equal to Mass ($m$) multiplied by a very large constant such
  as the speed of light squared ($c^2$).

In regard to the title: No, and just because something is moving away from you at, say twice the speed of light, does not mean that it is moving at twice the speed of light. Space can move without the things inside it moving.
In regard to the individual points:

  
*
  
*does this equation mean masses are just condensed energy?
  

No, it simply means energy and mass are interchangeable and mass converts into a lot of energy.


  
*And does this mean that the extra energy an object has when traveling at light speed simply becomes mass?
  

No, the equation itself says nothing about movement or speed, or even the speed of light. Things don't just get to light speed, you need to apply energy to a mass to accelerate it.
Mathematically, based on this formula there is no reason that you can't travel at or faster than the speed of light.
Look at the formula for accelerating masses and consider that in order to get to light speed the kinetic energy has to come from somewhere (e.g. blow something up - check the mass to kinetic energy conversion ratio.. it's not good!), and if you do the sums you will find the amount of energy (or mass to blow up and convert it into energy) you have to give a mass to get it to that speed is infeasible. 


  
*So then are all the masses just energy traveled at light speed?
  

Nope.


  
*If so, doesn't light suppose to be relatively stationary for us?
  

No, because you aren't travelling at the speed of light.
A: The famous equation $E = mc^2$ is actually just a special case of the relativistic equation for the total energy:
$$ E^2 = p^2c^2 + m^2c^4 \tag{1} $$
where $p$ is the relativistic momentum and $m$ is the (constant) rest mass:
$$ p = \frac{mv}{\sqrt{1 - v^2/c^2}} $$
For an object that isn't moving $p=0$ and equation (1) becomes:
$$ E = mc^2 $$
which is what you started with. But for a moving object we need to include the $p^2c^2$ term and this is what accounts for the extra energy associated with the motion. So there's no weird effect of the extra energy of a moving object becoming mass.
Incidentally this equation applies to light as well. For light the mass $m$ is zero and equation (1) becomes:
$$ E = pc $$
This might be more recognisable if we make the substitution $p=h/\lambda$ to get:
$$ E = \frac{hc}{\lambda} = h\nu $$
A: 
does this equation mean masses are just condensed energy?

No, it means that mass is just another form of energy, just like heat, motion, electric attraction, etc.
For example, the energy of a charged sphere is
$$
E=\frac{3}{5}\frac{Q^2}{R}
$$
This equation doesn't mean that charge is just condensed energy; it means that charged objects have energy.
Similarly, the energy of an object at rest is
$$
E=mc^2
$$
and this doesn't mean that mass is condensed energy; it means that massive objects have energy.

And does this mean that the extra energy an object has when traveling at light speed simply becomes mass? So then are all the masses just energy traveled at light speed?

This doesn't make much sense: the only object that travel at the speed of light is, well, light. Nothing else can travel that fast.
andynitrox suggested that OP is probably talking about the "relativistic mass", i.e., the fact that an object's mass increases when moving close to the speed of light. Note that this is a historical mistake: the mass of an object is independent of its state of motion. Mass does not increase with speed.

If so, doesn't light suppose to be relatively stationary for us?

Why would it? it does not: it travel very fast. And we can measure its speed, and it turns out to be $3\ 10^8\ \mathrm{m/s}$. This is not at all stationary, it's very very fast!
So, what does $E=mc^2$ mean?
Now that I've addressed your questions, let me try to answer to the important one: what is the meaning of $E=mc^2$.
It turns out that we people made some mistakes when we choose how to measure things in physics. We had to measure distances and we choose that we should compare the length of an object with a prototype bar to which we arbitrarily assigned the length "1 meter". Let's say I want to have a barn built in my land. I'll tell the engineer "I want it 3 meters tall". This means that my barn should be thrice as tall as that platinum-iridium bar we forged some time ago.
But now let's say that physicists, back in the day, chose another prototype bar, half as large as the previous one, and call that length "1 AFT", that is, 1 meter = 2 AFT. In this case, I'll tell the engineer that my barn should be "6 AFTs tall". As you can see, the actual value of the height depends on arbitrary conventions.
Well, the truth is, scientists choose some arbitrary conventions, and they did it wrong. It turns out that things are way easier (in physics, not in every day life) if we choose another convention for length, one that is not arbitrary but has a reason: we choose the unit of length such that $c=1$ instead of $c=3\ 10^8\ \mathrm{m/s}$. This may look like unusual, because $c=1$ doesn't have units any more, but bear with me, it is convenient. Now, how tall should my barn be?
Note that
$$
1=c=3\ 10^8\ \mathrm{m/s}\quad\Leftrightarrow \quad 1\ \mathrm{m}=\frac{1}{3\ 10^8}\mathrm{s}=3.33\ 10^{-9}\ \mathrm{s}
$$
and therefore my barn is $3\ \mathrm{m}=10^{-8}\ \mathrm{s}$ tall. We measure a length with units of seconds! I should tell the engineer "I want a ten-nanoseconds tall barn". But why would we want to do this!?
Well, if $c=1$ then many equations are way simpler, such as for example
$$
E=m
$$
Now you can see what $E=mc^2$ really means: mass and energy are the same thing. The factor of $c^2$ is just there because we choose a bad prototype bar. Had we been more clever, it wouldn't be there. But wait! I said in the first paragraph of this post that mass and energy are not the same thing, so what's going on? Are they or are they not?
Well: no, they are not. They are not because $E=mc^2$ is not the end of the story. The true equation is more like this:
$$
E=\frac{m}{\sqrt{1-v^2}}+\text{electric energy}+\text{magnetic energy}+\text{gravitational energy}+\cdots
$$
where we must include all forms of energy. In particular, note that the first term depends on $\boldsymbol v$, that is, the velocity of the particle. Now, what do we get if the particle is at rest, and far from anything else, that is, isolated? Well, in that case, we get $E=m$ back. So, is mass the same as energy? no, the energy of a particle includes all forms of energy. Mass is the energy of a particle that is at rest and far from any other particle. This is the true definition of mass, the one that you should remember. With this definition, it's easy to see that mass does not depend on velocity: it is defined as the energy of an object at rest, so how could it even depend on velocity?
