Hypotheses and Fallacies

I've been sitting on this hypothesis for some time now. It's full of fallacies, but it shows that there is something I know and can think independently about.

So, this is how it goes.

Einstein's theories of relativity explain something called "time dilation" — the idea that time slows down as the object speeds up. It also predicts that no object can go faster than the speed of light.

And in tandem with a hypothesis I was discussing with a friend a few months ago, I tried to think about time travel as a function of speed (yes, think about. Never let it be said that philosophy is dead.). Here are my conclusions:

1. If time slows down as we approach the speed of light, there has to be a point where time stops. Then there are also points where time should start going backwards. This point comes past the speed of light, which is prohibited by the laws of physics. The speed of light is the cosmic speed limit.
2. So, the speed of light is that speed at which time becomes meaningless. Sure, we talk about light taking time to reach other objects in the universe, but that's because it is we who perceive time. From the perspective of light, it means nothing. For photons, there is no such thing as time. Thus why we have one photon in more than one place at the same time, or vice versa. 
3. So, essentially, if we want to travel backwards in time, we have to go faster than the speed of light. Explains why time travel is impossible.
4. If we want to understand the true nature of time – what it is, as opposed to what it does – we have to study it from the perspective of photons. And in a notion akin to relativity of motion through space, the motion of time, in essence, the speed of time on Earth (or anywhere in the universe) can be measured in relation to light.

There are some problems with this, though.

The first is that light itself doesn't always travel at the speed of light. And yet time is meaningless for it even at slower speeds. One could look to the massless nature of photons for a possible solution.

The second is kind of mathematical. We usually quantify change with respect to something. Usually that "something" is time. But when it is the speed of time itself that needs to be measured, what do you measure it with respect to? What property of light? Because the parameters we speak of here are set at zero. And every schoolchild knows that division by zero is undefined.

Well, it's a step in the process of becoming an astrophysicist, at least.