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The effect of substituting iron and zinc for cobalt in CaBaCo$_4$O$_7$ has been investigated using neutron diffraction and x-ray absorption spectroscopy. The orthorhombic distortion present in the parent compound CaBaCo$_4$O$_7$ decreases with increasing the content of either Fe or Zn. The samples CaBaCo$_3$ZnO$_7$ and CaBaCo$_{4-x}$Fe$_x$O$_7$ with $x \leq 1.5$ are metrically hexagonal but much better refinements in the neutron diffraction patterns are obtained using an orthorhombic unit cell. The two types of substitution have opposite effects on the structural and magnetic properties. Fe atoms preferentially occupy the sites at the triangular layer. Thus, the replacement of Co by Fe supresses the ferrimagnetic ordering and CaBaCo$_{4-x}$Fe$_x$O$_7$ samples are antiferromagnetically ordered with a new propagation vector k=(1/3,0,0). However, the Zn atoms prefer occupying the Kagome layer, which is very detrimental for the long range magnetic interactions giving rise to a magnetic glass. The oxidation state of iron and zinc is found to be 3+ and 2+, respectively, independently of the content. Therefore, the average Co oxidation state changes accordingly with the Fe$^{3+}$ or Zn$^{2+}$ doping. Also, x-ray absorption spectroscopy data confirms the different preferential occupation for both Fe and Zn cations. The combined information obtained by neutron diffraction and x-ray absorption spectroscopy indicates that cobalt atoms can be either in a fluctuating Co$^{2+}$/Co$^{3+}$ valence state or, alternatively, Co$^{2+}$ and Co$^{3+}$ ions being randomly distributed in the lattice. These results explain the occurrence of local disorder in the CoO$_4$ tetrahedra obtained by EXAFS. An anomaly in the lattice parameters and an increase in the local disorder is observed only at the ferrimagnetic transition for CaBaCo$_4$O$_7$ revealing the occurrence of local magneto-elastic coupling.