Bypass transition, momentum and passive scalar transports in an initially laminar low Reynolds number channel flow with a specific roughness morphology are investigated by direct numerical simulations. The roughness elements are square bars of large heights $k$. Turbulence cannot be triggered in an initially laminar flow without external noise, when the bars extend the entire width of the channel. A staggered configuration is necessary to break up the spanwise symmetry, in which case a pseudo-fully developed rough regime sets up and self-sustains near and below the subcritical Reynolds number. The critical parameter is the shift $s$ between two consecutive staggered bars spanning half the width of the channel. A small shift $s/k$ is enough to trigger the turbulent field. Momentum and scalar fields are analysed for different $s/k$ configurations. The Townsend similarity hypothesis postulating that the outer layer is insensitive to the roughness effects, and that the rough- and smooth-wall statistics collapse in the outer layer, holds well for the momentum field despite the large roughness heights. A particular attention is paid to the deviation of the scalar statistics from the Townsend hypothesis. There is a dissimilarity between the fluctuating temperature and the velocity fields. The Reynolds analogy does not hold stricto sensu. Wake-induced terms determined through the double-averaging procedure play an important role in the rough sublayer. For instance, a significative production of the fluctuating spanwise velocity intensity, which is absent in the canonical flow, appears as a wake-induced term at small shifts. This is solely due to the imposed spanwise asymmetry. The nature, the generation and the self-sustaining mechanisms of the coherent structures near and between the roughness elements are analysed in detail in different configurations. There is a substantial increase of the Nusselt number at particularly low Reynolds numbers.