In my recolloection I don't think antimatter is moving backwards in time.. Where would it end up once it gets back to the big bang?(Antimatter was created at the same time as matter, so it should probably have made its way back there by now)
Time Travel And Antimatter

The Feynman-Stueckelberg interpretation that antiparticles are particles travelling backwards in time is considered entirely valid.
If you compare the Feynman diagrams for an electron being deflected by photons, and the diagram for an electron and a positron annihilating into two photon, it is clear there is not much difference. In the annihilation diagram, you could think the deflection is so strong it knocks the electron back in time! [Although you could draw an annihilation diagram or a deflection diagram with only one photon, as there is no way to conserve energy-momentum in this case, all real interactions have two vertices like these ones].
It is amusing to think about the annihilation of an electron and a positron (top diagram above) as being a time machine, where the positron is considered to be the same particle (reasonable from the diagram). Of course since it moved backwards in time after the annihilation, we would have seen it as the positron that was about to annihilate the electron. But it's not very practical as a time machine, as to "send an electron back in time", what you need to do is find any positron, annihilate the two particles, and then claim that the positron you had used was the electron being sent back in time.
Given this view, I suppose the answer to pawn_slayer666's question is "yes".

I tried to understand Feynman diagrams for a while, but they were really complicated, some of the wikipedia examples.
In the second picture, does it mean that the first photon hit the positron in its future, then another photon hit it before the first one did from its point of view. If there were an antimatter copy of myself and I talked to it, ignoring that one of us would blow up due to environmental conditions (air is matter), would we be able to understand each other? Or would speech of each of us be reversed from the other's perspective? Would my future be other me's past and vice versa?

Well, the first thing about Feynman diagrams is that every straight or wavy line is the graph of a particle moving through space (only one dimension on the diagram, to make it possible to put on a page). So if you follow the arrow of time (upward on my diagrams) you see things changing over time.
The second thing is that wherever you have a vertex (three lines meeting) you have some sort of event taking place, which is either two particles coming in and one going out, or vice versa. So for example, an electron emits a photon, and continues moving, but in a different direction.
The first thing that confuses this is that if you try to make such a vertex, you can't make both the momentum and the energy add up. But quantum mechanics saves the day because the uncertainty principle allows energy to not add up for a short time. The line right in the middle of each diagram is very short, and is where this temporary discrepancy occurs. In practice all you see is the electron and positron going in and two photons coming out in one case, or a photon deflecting an electron and bouncing back (called "scattering") in the other one - the little bit in the middle is too small to see.
As for how an antimatter version of pawn_slayer666 would behave, the arrow of time that is relevant is the arrow of entropy. If you watch an antimatter system, entropy progresses in the same direction as usual. For example, if you had an antimatter box full of antimatter gas and the gas was hotter in one region, it would tend to mix so that the gas all ended up at the same temperature. Generalising, chemical reactions would progress in the normal time direction in the antimatter pawn_slayer666, generating heat from burning fuel rather than generating fuel from heat in a way that would violate the 2nd law of thermodynamics. Generalising further, antimatter pawn_slayer666 would not speak backwards!
The arrow of entropy is a very important thing in physics, since most of the laws of physics are time reversible (the only quite minor exception is the weak interaction). But even a macroscopic system where only time reversible laws apply (general relativity and quantum electrodynamics, say), the arrow of entropy applies. But how can it apply in one direction and not the other?
Well, it's all about information. Something that is ordered tends to become more disordered, as a whole, because there are far more ways to become disordered than to become ordered. A low entropy state is one that is special (eg hot gas on one side, cold on the other) and a high entropy state (eg all gas the same temperature) is one that is nondescript. Some people consider it a big mystery that the universe started in a very special, low entropy state, which allows the arrow of entropy to progress for many billions of years.
I recall antimatter being matter moving backwards in time. I also know that most time machines are said to be able to move backwards in time, rather than making a wormhole (at least in the movie click, time could rewind). But wouldn't that mean that whatever it rewinding is actually antimatter. This would mean a time machine is actually an Einstein reactor? (Einstein reactor is what I call anything that converts E=mc^2 perfectly)