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 \mu m 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- \mu m dust continuum data . Results : All the LABOCA cores in the region covered by our SABOCA map were detected at 350 \mu m. The strongest 350 \mu m 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 \mu m flux density ratios , we determine dust temperatures of T _ { dust } \simeq 7.9 - 10.8 K , and dust emissivity indices of \beta \sim 0.5 - 1.8 . The CO depletion factors are in the range f _ { D } \sim 1.6 - 10.8 . The degree of deuteration in N _ { 2 } H ^ { + } is \simeq 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 \sim 2 - 6 \times 10 ^ { -8 } and \sim 2.6 \times 10 ^ { -17 } -4.8 \times 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 .