(LRDs)$^2$: The Low-ReDshift Little Red Dots Survey. II. DESI DR1 Sample

JWST has revealed a substantial population of "Little Red Dots" (LRDs) at $z>4$, challenging conventional AGN frameworks. However, the low-redshift regime remains largely unexplored. In the second paper of the (LRDs)$^2$ series, we present a systematic selection from DESI DR1 and identify 27 LRDs at $z=0.2-0.9$, yielding a number density lower limit of $7.5 \times 10^{-10}$ cMpc$^{-3}$. We conducted near-IR spectroscopic follow-up observations for 18 of them, revealing their full SED shapes and emission lines. These low-$z$ LRDs share the hallmark properties of their high-$z$ counterparts: compact morphology, V-shaped UV-optical continua, broad Balmer emission with extreme decrements (median H$\alpha$/H$\beta \sim 16$), frequent Balmer absorption (67%), and blackbody-like optical-to-near-IR continua. All have low metallicity, occupy the same regions in the BPT diagram as high-$z$ LRDs, and have softer ionizing spectra than typical AGNs. The consistency between low-$z$ and high-$z$ LRD properties indicates the same physical processes at work. The correlation between broad-line Balmer luminosity and $L_{5100}$ deviates from that of local type-1 AGNs, limiting the direct application of local BH mass calibrations. Ionized [O III] outflows are ubiquitous (78%). One LRD at $z=0.196$, J1717+3807, shows robust long-term variability in $i$ and WISE bands. The optical-to-NIR continua of LRDs reveal a wide range of temperatures $\sim 2000-4700$ K (peak $0.6-1.5$ $\mu$m), with a subset showing cooler and larger envelopes than those at high $z$. Low-$z$ LRDs serve not only as proximate laboratories for probing the nature of LRDs, but also trace the cosmic evolution of this population from the cosmic dawn to the present day.