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The present study aims to characterise the physical and chemical properties of the protostellar core Orion B9-SMM3. The APEX telescope was used to perform a follow-up molecular line survey of SMM3. The following species were identified from the frequency range 218.2-222.2 GHz: $^{13}$CO, C$^{18}$O, SO, para-H$_2$CO, and E$_1$-type CH$_3$OH. The on-the-fly mapping observations at 215.1-219.1 GHz revealed that SMM3 is associated with a dense gas core as traced by DCO$^+$ and p-H$_2$CO. Altogether three different p-H$_2$CO transitions were detected with clearly broadened linewidths (8.2-11 km s$^{-1}$ in FWHM). The derived p-H$_2$CO rotational temperature, $64\pm15$ K, indicates the presence of warm gas. We also detected a narrow p-H$_2$CO line (FWHM=0.42 km s$^{-1}$) at the systemic velocity. The p-H$_2$CO abundance for the broad component appears to be enhanced by two orders of magnitude with respect to the narrow line value ($\sim3\times10^{-9}$ versus $\sim2\times10^{-11}$). The detected methanol line shows a linewidth similar to those of the broad p-H$_2$CO lines, which indicates their coexistence. The CO isotopologue data suggest that the CO depletion factor decreases from $\sim27\pm2$ towards the core centre to a value of $\sim8\pm1$ towards the core edge. In the latter position, the N$_2$D$^+$/N$_2$H$^+$ ratio is revised down to $0.14\pm0.06$. The origin of the subfragments inside the SMM3 core we found previously can be understood in terms of the Jeans instability if non-thermal motions are taken into account. The estimated fragmentation timescale, and the derived chemical abundances suggest that SMM3 is a few times $10^5$ yr old, in good agreement with its Class 0 classification inferred from the spectral energy distribution analysis. The broad p-H$_2$CO and CH$_3$OH lines, and the associated warm gas provide the first clear evidence of a molecular outflow driven by SMM3., 25 pages, 6 figures, 4 tables; accepted for publication in Astrophysics and Space Science