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One homoleptic (<b>1</b>) and three heteroleptic (<b>2</b>–<b>4</b>) palladium(II) complexes were synthesized and characterized by various physicochemical techniques, i.e., elemental analysis, FTIR, Raman spectroscopy, ¹H, ¹³C, and ³¹P NMR. Compound <b>1</b> was also confirmed by single crystal XRD, showing a slightly distorted square planar geometry. The antibacterial results obtained via the agar-well diffusion method for compound <b>1</b> were maximum among the screen compounds. All the compounds have shown good to significant antibacterial results against the tested bacterial strains, <i>Escherichia coli, Klebsiella pneumonia,</i> and <i>Staphylococcus aureus,</i> except <b>2</b> against <i>Klebsiella pneumonia</i>. Similarly, the molecular docking study of compound <b>3</b> has shown the best affinity with binding energy scores of −8.6569, −6.5716, and −7.6966 kcal/mol against <i>Escherichia coli, Klebsiella pneumonia,</i> and <i>Staphylococcus aureus</i>, respectively. Compound <b>2</b> has exhibited the highest activity (3.67 µM), followed by compound <b>3</b> (4.57 µM), <b>1</b> (6.94 µM), and <b>4</b> (21.7 µM) against the DU145 human prostate cancer cell line using the sulforhodamine B (SRB) method as compared to cisplatin (>200 µM). The highest docking score was obtained for compounds <b>2</b> (−7.5148 kcal/mol) and <b>3</b> (−7.0343 kcal/mol). Compound <b>2</b> shows that the Cl atom of the compound acts as a chain side acceptor for the DR5 receptor residue <i>Asp B218</i> and the pyridine ring is involved in interaction with the <i>Tyr A50</i> residue via arene-H, while Compound <b>3</b> interacts with the <i>Asp B218</i> residue via the Cl atom. The physicochemical parameters determined by the SwissADME webserver revealed that no blood-brain barrier (BBB) permeation is predicted for all four compounds, while gastrointestinal absorption is low for compound <b>1</b> and high for the rest of the compounds (<b>2</b>–<b>4</b>). As concluding remarks based on the obtained in vitro biological results, the evaluated compounds after in vivo studies might be a good choice for future antibiotics and anticancer agents.