We present results of a blind search for Galactic HI 21-cm absorption lines toward 19130 radio sources, using 390 pointings of MALS, each pointing centered on a source brighter than 200mJy. We detected 3640 HI absorption features. This represents the largest Galactic HI absorption line catalog to date. Based on the strong correlation between the HI 21-cm emission line column densities (NHI) and the visual extinction (A_V) measured toward the pointing center, along with the confinement of the absorption features to a narrow range in radial velocities (-25<v_LSR_[km/s]<+25), we infer that the detected absorption lines form a homogeneous sample of HI clouds in the local interstellar medium (LISM). The HI 21-cm absorption optical depth is linearly correlated to NHI and AV, up to AV of about 1 mag. Above this threshold, AV traces the total hydrogen content, and consequently, AV and NHI scale, differently. The slopes of NHI distributions of central sight lines with HI 21-cm absorption detections and non-detection differ at >2{sigma}. A similar difference is observed for H2 detections and non-detections in damped Lyman-alpha systems at z>1.8, implying that turbulence-driven WNM-to-CNM conversion is the common governing factor for the presence of HI 21-cm and H2 absorption. Through a comparison of central and off-axis absorption features, we find that the slope of rms fluctuations in the optical depth variations in the quiescent gas associated with LISM is shallower than the earlier measurements in the disk. The densities (20-30cm^-3^) inferred from the optical depth variations are typical of the CNM values. The negligible velocity shifts between central and off-axis absorbers are in line with the hypothesis that the CNM and LNM clouds freeze out of the extended WNM phase.