To answer your questions:
- Yes, fibreoptics transfer light.
- Maybe. I'll discuss that now
Fibreoptics are strands of glass, they're CRAP at going around corners, I mean seriously crap, communications fibre is VERY THIN. Even then it can't go around bends well, they test it at every stage during laying. However with communications stuff the path matters (more bouncing around inside (due to total internal reflection) causes a larger path, so another signal may get there first). However any bends do put strain on the glass.
A thicker strand of glass would be needed. Electricity has none of these problems.
Additionally you can't "wire" stuff in series or parallel with fibreoptics, it's point-to-point. So you'd have to have an expensive "junction" that siphoned some of the light at each lamp, which would make them get progressively dimmer.
It also is a single point of failure, some git could simply cut this thick bundle of glass and it'd be a bitch to replace. (although America found a way with the cables crossing the ocean, I recall reading somewhere they'd managed to 'tap' the cables, which was something I'd previously laughed off as impossible) Unlike wire, which you can simply strip, twist (tape, and/or solder) and then cover back up.
As you can see, not a practical idea.
Found some info on the fibretapping I mentioned:
Wiki
For "full disclosure" sadly so did GCHQ (the UK version)