Background: Derivatives of Pyrido[2,3-d]pyrimidine-6-carboxylate are promising multi-target scaffolds. This study focused on synthesizing 16 amino-functionalized derivatives and evaluating their dual anticancer and antibacterial activities, supported by mechanistic and computational analyses. Objectives: Design and synthesize derivatives, evaluate cytotoxicity against HeLa, HepG-2, and MCF-7 (selectivity against WI-38), investigate EGFR^WT and EGFR^T790M inhibition, assess cell cycle, apoptosis, and migration effects, antibacterial efficacy against E. coli and P. aeruginosa, and perform in silico ADMET, docking, molecular dynamics, DFT, and antiviral predictions. Methods: Synthesized 16 derivatives; tested for cytotoxicity, EGFR inhibition, cell cycle, apoptosis, migration; assessed antibacterial activity; performed ADMET profiling, molecular docking, molecular dynamics, and DFT calculations. Results: Derivatives 1, 2, and 7 showed highest cytotoxicity (IC₅₀ = 3.98–17.52 μM; WI-38 IC₅₀ = 64.07–81.65 μM). Compound 1 potently inhibited EGFRWT (IC₅₀ = 0.093 μM) and EGFRT790M (IC₅₀ = 0.174 μM), induced G0/G1 arrest (74.86%) and apoptosis (26.37%), and reduced MCF-7 migration (69.63%). Moderate antibacterial activity observed (MIC = 50 μg/mL). ADMET indicated favorable pharmacokinetics, low CYP inhibition, negative mutagenicity, and oral toxicity class III. Molecular dynamics confirmed stable binding (EGFRWT RMSD 3 Å; EGFRT790M 3.5–4.6 Å) with persistent hydrogen bonds. In silico antiviral evaluation suggested strong binding to HCV NS5A (–9.36 kcal/mol), SARS-CoV-2 Mpro (–9.82 kcal/mol), and E.coli DNA gyrase (–10.25 kcal/mol). Conclusions: Compound 1 exhibits dual anticancer and antibacterial activity, supported by mechanistic and computational analyses, highlighting pyrido[2,3-d]pyrimidines as promising multi-target therapeutic scaffolds.