When John and Jade enter the Yellow Yard, she explains to him that it will take three years to cross the entire distance. She says that it will take them this long because you cannot go faster than the speed of light. According to the famous equation E=MC^2, energy is equal to mass moving at the speed of light squared. Wouldn't this mean that the ship could move at it's fastest just slower than the speed of light squared, which is many times faster than just sub the speed of light?
No, the fastest possible speed for a spaceship is just short of the speed of light.
E=mc2 is talking about your energy at rest. You need an equation for energy at relativistic speeds:
E = mc2/sqrt(1−v2/c2)
where E is the relativistic total energy, m is mass, c is the speed of light, and v is your speed. As v approaches c, E approaches infinity. If v=0, this equation reduces to E = mc2.
Note that people sometimes like to define mass m to increase as you approach the speed of light, but in the equations above, m is the “rest mass” and does not change with speed.
This is further complicated by the idea of reference frames and time dilation, so that the duration of a voyage at near light speed is different for someone on the ship than it is for someone who didn’t go. However, it appears that the comics don’t take this into account, so we can skip that part. If you want to read about it anyway, here are a couple links:
Without reading the entire series, it appears that the in-universe physics is a sort of hybrid of relativity and Newtonian mechanics: the speed of light is an arbitrary maximum speed, and time dilation does not occur. Or perhaps I misunderstood the context in the text that I read.
This all assumes that the Yellow Yard is three light-years across. I couldn’t verify whether that was true.