This paper presents a mathematics-focused AI iterative prediction framework that combines Extreme Gradient Boosting (XGBoost) for nonlinear function approximation with nonlinear autoregressive model with exogenous inputs (NARXs) for time-series modeling, applied to analyzing the Remaining Useful Life (RUL) and availability of Unmanned Aerial Vehicle (UAV) Brushless DC (BLDC) motors. The framework integrates nonlinear regression, temporal recursion, and survival analysis into a unified system. The dataset includes five UAV motor types, each recorded for 10 min at 20 Hz, totaling approximately 12,000 records per motor for validation across these five motor types. Using grouped K-fold cross-validation by motor ID, the framework achieved mean absolute error (MAE) of 4.01 h and root mean square error (RMSE) of 4.51 h in RUL prediction. Feature importance and SHapley Additive exPlanation (SHAP) analysis identified temperature, vibration, and HI as key predictors, aligning with degradation mechanisms. For availability assessment, survival metrics showed strong performance, with a C-index of 1.00 indicating perfect risk ranking and a Brier score at 300 s of 0.159 reflecting good calibration. Additionally, Conformalized Quantile Regression (CQR) enhanced interval coverage under diverse operating conditions, providing mathematically guaranteed uncertainty bounds. The results demonstrate that this framework improves both accuracy and interpretability, offering a reliable and adaptable solution for UAV motor prognostics and maintenance planning.