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This study presents a comprehensive multi-dimensional analytics framework for examining customer engagement, product utilization, and retention behaviour across 10,000 European bank customers. Drawing on a richly engineered dataset comprising 59 analytical features derived from 14 raw variables, the research employs an exploratory data analytics (EDA) paradigm augmented by a proprietary Relationship Strength Index (RSI), a four-tier Engagement Classification system, and a logistic-inspired Retention Risk Scoring model. The dataset yields an overall churn rate of 20.37% (n=2,037), with Germany exhibiting the highest regional churn at 32.44% against France (16.15%) and Spain (16.67%). Inactive customers churn at 26.85% versus 14.27% for active members, producing an Engagement Retention Ratio (ERR) of 1.88. The product utilization analysis reveals a paradoxical non-linear pattern: dual-product customers exhibit the lowest churn (7.58%), while customers holding three or four products demonstrate dramatically elevated churn rates of 82.71% and 100%, respectively. The RSI composite score demonstrates the strongest negative correlation with churn (r = -0.271), outperforming all individual predictors. Five strategic KPI flags are operationalised: High-Balance Disengaged (n=1,247; churn=30.47%), Sticky Customers (n=1,015; churn=9.26%), Silent Churn Risk (n=828; churn=33.45%), Salary-Balance Mismatch (n=891), and Wealth Engagement Gap (n=1,231). Findings provide actionable intelligence for retention strategy design in the European banking sector.