This work reports unsteady pressure measurements in a non-premixed backward-facing step combustor over a wide range of operating conditions and lengths of the combustor duct, ranging from generation of low-amplitude noise without appreciable feedback from the natural acoustic modes of the duct, to excitation of high-amplitude discrete tones due to flow-acoustic lock-on. Since these unsteady pressure signals could predominantly arise from the natural acoustic modes of the duct or due to local flow fluctuations in the vortex shedding process downstream of the dump plane, dimensionless groups such as the Helmholtz and Strouhal numbers are formed, whose variations with Reynolds number help distinguish the duct acoustic modes from the vortex shedding modes. As the flow velocity is increased, the observed dominant frequencies shift from those corresponding to the latter to those of the former, whereupon, the flow-acoustic lock-on shifts between one vortex shedding mode to the other, as opposed to the vortex shedding locking on to the natural acoustic mode of the duct observed under cold-flow conditions. A map of the onset of instabilities is presented for the conditions tested. The map is in a domain of the equivalence ratio of the fuel and air flows to the ratio of the Strouhal number to the Helmholtz number, i.e., the ratio of the flow time-scale to the acoustic time-scale. These two quantities contain all the parameters of the problem, and indicate an instability map for a particular location of injection of the fuel, i.e., mode of combustion, in a given combustor geometry. The total chemiluminescent intensity fluctuations show the same dominant frequencies as the acoustic oscillations under all conditions, signifying the vortex-combustion interaction prevalent always. The cold flow PIV results show that large scale structures are present in the recirculation zone and the length of the recirculation zone is constant for the step height used. Further chemiluminescence and reacting-flow PIV measurements show the processes such as vortex pairing and merging that influence the heat release fluctuations.