Saying something, anything, moving at light speed has infinite mass assumes light moves infinitely fast and/or light has no mass, neither of which is true. We know the speed of light in a vacuum is approximately 299,792,458 meters/second, debunking that light is infinitely fast. Energy is the motion of matter, and light is no exception. Even light is affected by gravity because the movement is connected to a particle. Normally you wouldn't notice this, but something with exceptional gravitational pull, like a black hole, makes it obvious. Also, the fact that light travels slower when other matter gets in the way adds to this.
If you are on a plane going 400 mph, you can stand up and throw a ball in the air. Neither you nor the ball is going to slam into the back of the plane because the plane and everything inside of it is moving together. Light travel would be basically the same as this, just moving faster. The only difference is that a light speed craft would likely not be using a propulsion system like we have today.
Also, assuming heat cannot be made orderly raises a new problem. If existence has existed forever, then all energy would be heat by now. Unless you are saying that one day everything sprang into existence from nothing, which also makes no sense. Everything comes from something. We just don't know how to make heat become orderly again without losing even more energy to heat. By extension, I propose that before the "big bang" was another big bang. A huge mass explodes, releasing all the matter and energy. this matter and energy combines into stars, planets, whatever. Slowly, gravity starts pulling everything back together. When the mass gets too dense, it can no longer contain the energy within and explodes. Then it starts all over again, and who is to say that there weren't other big bangs in the universe. Everything goes in cycles when you get down to it.