We present a Neural-Driven Multi-Band Processor (NDMP), a differentiable audio processing framework that augments a static six-band Parametric Equalizer (PEQ) with per-band dynamic range compression. We optimize this processor using neural inference for two tasks: Automatic Equalization (AutoEQ), which estimates tonal and dynamic corrections without a reference, and Production Style Transfer (NDMP-ST), which adapts the processing of an input signal to match the tonal and dynamic characteristics of a reference. We train NDMP using a self-supervised strategy, where the model learns to recover a clean signal from inputs degraded with randomly sampled NDMP parameters and gain adjustments. This setup eliminates the need for paired input-target data and enables end-to-end training with audio-domain loss functions. In the inference, AutoEQ enhances previously unseen inputs in a blind setting, while NDMP-ST performs style transfer by predicting task-specific processing parameters. We evaluate our approach on the MUSDB18 dataset using both objective metrics (e.g., SI-SDR, PESQ, STFT loss) and a listening test. Our results show that NDMP consistently outperforms traditional PEQ and a PEQ+DRC (single-band) baseline, offering a robust neural framework for audio enhancement that combines learned spectral and dynamic control.