Lithium-ion batteries are utilized in electric vehicles (EVs), and accurate predictions of battery state of charge (SOC), state of health (SOH), and remaining useful life (RUL) are needed to ensure reliability, security, and durability of these batteries. This study provides a hybrid deep learning (DL) system, termed as Neural Basis Expansion Variational Ladder Transformer (NBE-VLT), integrating Polar Fox Optimization (PFO) for effective global hyperparameter tuning to produce accurate SOC, SOH, and RUL predictions from raw battery cycle data. The preprocessed battery cycle data were sent through a series of steps before the analysis to increase data features and reliability; these steps involved removing outliers, encoding features, normalizing the data, and aligning time. The Neural Basis Expansion (NBE) layer decomposes the battery's temporal signals using an adaptive basis function. The Variational Ladder Autoencoder (VLAE) generates hierarchical latent representations capable of learning and capturing degradation patterns and uncertainty information from battery data. In addition, a transformer encoder is used to learn long-range temporal dependencies, and an attention fusion mechanism combines features at different scales to produce accurate estimates of SOC, SOH, and RUL. The efficiency of the proposed model is shown through experimental evaluation conducted with the National Aeronautics and Space Administration (NASA) battery datasets, achieving SOC predictions with R2 of 0.9943, root mean squared error (RMSE) of 0.0225, mean absolute error (MAE) of 0.0164, and mean absolute percentage error (MAPE) of 1.64%. The SOH prediction achieved an R2 of 0.9606, RMSE of 0.0414, MAE of 0.0243, and MAPE of 2.43%, whereas RUL predictions achieved an R2 of 0.9936, RMSE of 0.0196, MAE of 0.0156, and MAPE of 1.56%. This indicates that the proposed framework, NBE-VLT-PFO, offers greater accuracy, robustness, and reliability for battery health forecasting.