Local Group (LG) galaxies have relatively accurate SFHs and metallicity evolution derived from resolved CMD modeling, and thus offer a unique opportunity to explore the efficacy of estimating stellar mass M$_{star}$ of real galaxies based on integrated stellar luminosities. Building on the SFHs and metallicity evolution of 40 LG dwarf galaxies, we carried out a comprehensive study of the influence of SFHs, metallicity evolution, and dust extinction on the UV-to-NIR color-$M/L$ (color-log$Upsilon_{star}$($lambda$)) relations and M$_{star}$ estimation of local universe galaxies. We find that: The LG galaxies follow color-log$Upsilon_{star}$($lambda$) relations that fall in between the ones calibrated by previous studies; Optical color-log$Upsilon_{star}$($lambda$) relations at higher metallicities ([M/H]) are generally broader and steeper; The SFH concentration does not significantly affect the color-log$Upsilon_{star}$($lambda$) relations; Light-weighted ages and [M/H] together constrain log$Upsilon_{star}$($lambda$) with uncertainties ranging from $lesssim$ 0.1 dex for the NIR up to 0.2 dex for the optical passbands; Metallicity evolution induces significant uncertainties to the optical but not NIR $Upsilon_{star}$($lambda$) at given light-weighted ages and [M/H]; The $V$ band is the ideal luminance passband for estimating $Upsilon_{star}$($lambda$) from single colors, because the combinations of $Upsilon_{star}$($V$) and optical colors such as $B-V$ and $g-r$ exhibit the weakest systematic dependence on SFHs, [M/H] and dust extinction; Without any prior assumption on SFHs, M$_{star}$ is constrained with biases $lesssim$ 0.3 dex by the optical-to-NIR SED fitting. Optical passbands alone constrain M$_{star}$ with biases $lesssim$ 0.4 dex (or $lesssim$ 0.6 dex) when dust extinction is fixed (or variable) in SED fitting. [abridged]
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