Context. Studies of dense molecular-cloud cores at (sub)millimetre wavelengths are needed to understand the early stages of star formation. Aims. We aim to further constrain the properties and evolutionary stages of dense cores in Orion B9. The prime objective of this study is to examine the dust emission of the cores near the peak of their spectral energy distributions, and to determine the degrees of CO depletion, deuterium fractionation, and ionisation. Methods. The central part of Orion B9 was mapped at 350 μm with APEX/SABOCA. A sample of nine cores in the region were observed in C 17 O(2−1), H 13 CO + (4−3) (towards 3 sources), DCO + (4−3), N 2 H + (3−2), and N 2 D + (3−2) with APEX/SHFI. These data are used in conjunction with our previous APEX/LABOCA 870-μm dust continuum data. Results. All the LABOCA cores in the region covered by our SABOCA map were detected at 350 μm. The strongest 350 μm emission is seen towards the Class 0 candidate SMM 3. Many of the LABOCA cores show evidence of substructure in the higher-resolution SABOCA image. In particular, we report on the discovery of multiple very low-mass condensations in the prestellar core SMM 6. Based on the 350-to-870 μm flux density ratios, we determine dust temperatures of T dust 7.9−10.8 K, and dust emissivity indices of β ∼ 0.5−1.8. The CO depletion factors are in the range f D ∼ 1.6−10.8. The degree of deuteration in N 2 H + is 0.04−0.99, where the highest value (seen towards the prestellar core SMM 1) is, to our knowledge, the most extreme level of N 2 H + deuteration reported so far. The level of HCO + deuteration is about 1-2%. The fractional ionisation and cosmic-ray ionisation rate of H 2 could be determined only towards two sources with the lower limits of ∼2−6 × 10 −8 and ∼2.6 × 10 −17 −4.8 × 10 −16 s −1 , respectively. We also detected D 2 CO towards two sources. Conclusions. The detected protostellar cores are classified as Class 0 objects, in agreement with our previous SED results. The detection of subcondensations within SMM 6 shows that core fragmentation can already take place during the prestellar phase. The origin of this substructure is likely caused by thermal Jeans fragmentation of the elongated parent core. Varying levels of f D and deuteration among the cores suggest that they are evolving chemically at different rates. A low f D value and the presence of gas-phase D 2 CO in SMM 1 suggest that the core chemistry is affected by the nearby outflow. The very high N 2 H + deuteration in SMM 1 is likely to be remnant of the earlier CO-depleted phase.