Proof of Snell's Law

Also, could someone possible explain how light can choose the shortest path always? Wouldn't that imply previous 'knowledge' of the start and end points? Which is definitely wrong... Thank again!

You're kind of looking at it wrong... The light doesn't need to know it's destination point to follow a path such that it reaches any point on the path in optimum time.

Think of it this way: if you point a light beam at an object in air, the beam will travel to that object because the path you pointed it along was the shortest possible (a straight line). Simples.
If, however, you pointed it at an object underwater the straight line path would no longer be optimum, so the light simply does not follow that path, it refracts on interaction with the water. At this stage, you don't nessecarily know the final destination point of the light, you can just be sure that wherever it goes (or even at any ponit along it's trajectory) it reaches in the shortest possible time.

In a sense, the principle doesn't so much tell you what the light does so much as tell you if a given path is valid under the laws of physics (or not).