Wolf-Rayet ([WR]) and weak emission-line ($wels$) central stars of planetary nebulae (PNe) have hydrogen-deficient atmospheres, whose origins are not well understood. In the present study, we have conducted plasma diagnostics and abundance analyses of 18 Galactic PNe surrounding [WR] and $wels$ nuclei, using collisionally excited lines (CELs) and optical recombination lines (ORLs) measured with the Wide Field Spectrograph on the ANU 2.3-m telescope at the Siding Spring Observatory complemented with optical archival data. Our plasma diagnostics imply that the electron densities and temperatures derived from CELs are correlated with the intrinsic nebular H$beta$ surface brightness and excitation class, respectively. Self-consistent plasma diagnostics of heavy element ORLs of N${}^{2+}$ and O${}^{2+}$ suggest that a small fraction of cool ($lesssim 7000$ K), dense ($sim 10^4-10^5$ cm$^{-3}$) materials may be present in some objects, though with large uncertainties. Our abundance analyses indicate that the abundance discrepancy factors (ADF$equiv$ORLs/CELs) of O${}^{2+}$ are correlated with the dichotomies between forbidden-line and He I temperatures. Our results likely point to the presence of a tiny fraction of cool, oxygen-rich dense clumps within the diffuse warm ionized nebulae. Moreover, our elemental abundances derived from CELs are mostly consistent with AGB models in the range of initial masses from 1.5 to 5M$_{odot}$. Further studies are necessary to understand better the origins of abundance discrepancies in PNe around [WR] and $wels$ stars.
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