We have performed survey-type observations in 1 mm continuum and molecular lines toward dense cores (32 prestellar + 7 protostellar) with an average density of $gtrsim$10$^5$ cm$^{-3}$ in the Taurus molecular clouds using the Atacama Large Millimeter/submillimeter Array-Atacama Compact Array (ALMA-ACA) stand-alone mode with an angular resolution of 6.$$5 ($sim$900 au). The primary purpose of this study is to investigate the innermost part of dense cores toward understanding the initial condition of star formation. In the protostellar cores, contributions from protostellar disks dominate the observed continuum flux with a range of 35-90% except for the very low-luminosity object. For the prestellar cores, we have successfully confirmed continuum emission from dense gas with a density of $gtrsim$3 $times$10$^5$ cm$^{-3}$ toward approximately one-third of the targets. Thanks to the lower spatial frequency coverage with the ACA-7 m array, the detection rate is significantly higher than that of the previous surveys, which have 0 or 1 continuum detected sources among large number of starless samples using the ALMA Main array. The statistical counting method tells us that the lifetime of the prestellar cores until protostar formation therein approaches the free-fall time as the density increases. Among the prestellar cores, at least two targets have possible internal substructures, which are detected in continuum emission with the size scale of $sim$1000 au if we consider the molecular line (C$^{18}$O and N$_2$D$^{+}$) distributions. These results suggest that small-scale fragmentation/coalescence processes occur in a region smaller than 0.1 pc, which may determine the final core mass associated with individual protostar formation before starting the dynamical collapse of the core with central density of $sim$(0.3-1) $times$ 10$^6$ cm$^{-3}$.
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