Translating brain activity into meaningful visual content has long been recognized as a fundamental challenge in neuroscience and brain-computer interface research. Recent advances in EEG-based neural decoding have shown promise, yet two critical limitations remain in this area: poor generalization across subjects and constraints to specific visual tasks. We introduce NEED, the first unified framework achieving zero-shot cross-subject and cross-task generalization for EEG-based visual reconstruction. Our approach addresses three fundamental challenges: (1) cross-subject variability through an Individual Adaptation Module pretrained on multiple EEG datasets to normalize subject-specific patterns, (2) limited spatial resolution and complex temporal dynamics via a dual-pathway architecture capturing both low-level visual dynamics and high-level semantics, and (3) task specificity constraints through a unified inference mechanism adaptable to different visual domains. For video reconstruction, NEED achieves better performance than existing methods. Importantly, Our model maintains 93.7% of within-subject classification performance and 92.4% of visual reconstruction quality when generalizing to unseen subjects, while achieving an SSIM of 0.352 when transferring directly to static image reconstruction without fine-tuning, demonstrating how neural decoding can move beyond subject and task boundaries toward truly generalizable brain-computer interfaces.