What exactly is information? Not the type which is transferred by lightwaves or whatnot, but entanglement type information, where if one proton does something, the other also does it. And since it has no exact mass that reality can grasp, why can't it travel at, or greater than, lightspeed?

The thing you're probably talking about is the quantum spin of the particle.

 

The reason it can't be faster than light is because for one particle to know the other had been changed or whatever needs a classical channel of communication between them, normally a laser, although you could use the postal services if you so wished

Actually, I was thinking of information on a more basic level, like the electron wave-particle duality type. For example, you set up an experiment in which you fire an electron from an electron gun at screen, where point A designates the most likely position the lil bastard will hit (say 50%), point B being second likely (pretend 30%) and finally point C, which is least likely (20%). So, if you shoot an electron at the screen X amount of times, and half those times, the electrons went to A, 30% of those times to B, how does those remaining electrons know they must land in the 20% area?

And how fast does information like that travel?

That's just randomness, the figures you suggest are not certain, they are probabilities... it may not be that way. In fact there's a minor chance they are all in C, its just the probability is too improbable to consider.