There is an on and an off state. Either the light is on or the light is off. That's how it translates into binary. Literally that's what binary data is: a single data-point is either on or off.
Not really. Yes, binary is on or off, but how the signal is read is it has a threshold for on/off. This is true for light, with fiber optics, and also electricity. The universe doesn't work on binary. We say "if the signal value is > X, do Y". Electrical engineering actually has to handle variability in the signal, while computer science just pretends it's actually binary.
Fiberoptics would technically work, but it's more material than you need because it would require running fiberoptic cables everywhere instead of just using hollow chromed tubes. Also, the quantity of light it can receive and transmit is limited to the thickness of the cable.
I'm not just making up hypotheticals. If your idea were better it would be used. Fiber optics to transfer light is actually a thing that's done. Here is a company selling that product, and there are many others, but I've also seen things about large structures using a custom solution too. It literally does work and is actually done in reality.