Classical optics is just the limiting case of quantum optics when the path length is much longer than the wavelength. In such a case quantum optics predicts basically zero probability to detect light on any path other than the classical path--which is classical optics. So classical optics doesn't say anything that's actually contradictory to quantum optics. It's just a special case.
It's classical ray optics that fails in the path-not-longer-than-wavelength regime. Classical wave optics works in that regime. Where classical techniques fail is at low brightness (because you start resolving individual photons).
Yes, but in classical wave optics you're no longer talking about "paths" as they appear in path integrals. Classical wave optics is basically quantum wave optics without the discreteness of detections, i.e., interpreting the wave as a straightforward EM field intensity instead of as a probability amplitude for detecting a photon.