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We present a comprehensive spectro-polarimetric and timing analysis of 12 black hole X-ray binaries, namely Cyg X$-$1, 4U 1630$-$47, Cyg X$-$3, LMC X$-$1, 4U 1957$+$115, LMC X$-$3, Swift J1727.8$-$1613, GX 339$-$4, Swift J151857.0$-$572147, IGR J17091$-$3624, MAXI J1744$-$294, and GRS 1915$+$105, using quasi-simultaneous observations from IXPE (Imaging X-ray Polarimetry Explorer), NICER (Neutron star Interior Composition Explorer), NuSTAR (Nuclear Spectroscopic Telescope Array), and AstroSat. Timing analyses reveal type-B and type-C quasi-periodic oscillations across different spectral states, often associated with episodic radio ejections. Broad-band (0.7-60 keV) spectral modelling, employing disc, Comptonization, and reflection components, reveals degeneracies in constraining disc-corona geometries. Polarimetric measurements in 2-8 keV band detect significant polarization degrees (PDs) ranging from 3 per cent-20.6 per cent (1.2 per cent-21.4 per cent) in harder (softer) states, with moderate to strong energy dependence, except for LMC X$-1$, Swift J151857.0-572147, and MAXI J1744$-$294, where no significant polarization is detected. We report polarization detections of Cyg X$-3$ (PD $\sim 21.4~{{\rm per\ cent}}$, soft intermediate state), LMC X$-3$ (PD $\sim 2.4~{{\rm per\ cent}}$, high-soft state), and IGR J17091-3624 (PD $\sim 9~{{\rm per\ cent}}$, low-hard state) using recent IXPE observations. A positive correlation is found between PD and Comptonized photon fraction ($cov_{\rm frac}$), while an anticorrelation is observed with disc-to-Comptonized flux ratio ($F_{\rm ratio}$) across spectral states. Combined timing, spectral, and polarimetric results, together with constraints from radio jet observations, suggest a radially extended corona within a truncated disc for Cyg X$-1$, Swift J1727.8-1613, IGR J17091-3624, and GX 339-4, whereas the disc-corona geometry remains poorly constrained for 4U 1957+115, LMC X$-3$, and 4U 1630-47. We discuss the implications of these findings for understanding accretion geometries and highlight prospects for future X-ray polarimetric studies.