This is the case in Multimode fiber, which is used for short distances (meters). For anything longer, single mode fiber is used and the core of the fiber guides the light. See https://garyherlache.wikispaces.com/Digital+Communications+F...
No, it does.
> Surely it can't go round any bend, then, though?
No, if you bend the fiber too much the light leaks out into the cladding.