In this work we present the implementation and study of time-multiplexed optical quantum networks. These incorporate the preparation of single-photon states, their manipulationin a dynamically reconfigurable circuitry and mode-resolving detection. With such a system we achieve versatile simulation capabilities for both wave-like as well as particle-like phenomena. The input states are generated in a parametric down-conversion (PDC) process engineered to be compatible with the time-multiplexing fibre network as well as to yield indistinguishableand pure photons which are required for quantum interference with high visibility. Employing fast-switching electro-optic modulators (EOMs), we can dynamically reconfigure the circuitry in terms of the splitting, routing and inhomogeneous losses to which thephotons are subjected. In this way, we can probe the effect of projective measurements during the evolution. The detection unit resolves the external (time bins) as well as the internal modes (polarisation), allowing for mode-dependent intensity and coincidence measurements. For describing the photons evolution we adopt the formalism of discrete-time quantum walks. Examining wave-like behaviour with coherent states, we investigate topologically-protected edge states as well as the effect of projective measurements. Probing particle-like effects with single-photon states, we conduct experiments revealing the interplay between the coherence properties of synthesized modes, the degree of mode resolution in the detection and the time-multiplexed quantum interference.