If I were in space looking at a star that just started producing light that was two light years away. Would I be able to see the light coming towards me?
You can't see the light coming towards you. But you can see it as soon as it reaches your position. That means, that if you're in space and there is a star which is 10 times far than the speed of light in seconds. And if that star emits the light "now", then you won't be able to know that whether the light is emitted "now" or not. Instead, after 10 seconds, you'll be able to see the light that was actually emitted by that start 10 seconds earlier.
This also means that you'll be looking at something that happened 10 seconds ago "at that star". If you ever took a telescope and looked at the sky, then you'll actually be looking at the lights that were emitted few seconds/minutes(depending on the power of telescope, whether it can see that far or not) ago.