Modern web and mobile platforms increasingly deploy complex anti-crawling mechanisms and enforce strict privacy regulations, making large-scale, compliant data acquisition a persistent challenge. In this paper, we propose a novel cross-platform adaptive web crawling framework that integrates deep reinforcement learning (DRL), federated learning (FL), and local differential privacy (LDP) to address the dual demands of operational efficiency and legal compliance. We formulate the crawling process as a Markov Decision Process (MDP) and leverage a PPO-based policy to enable dynamic decision-making under adversarial conditions, including CAPTCHA triggers, tokenized APIs, and platform switching. The system adopts a privacy-by-design architecture: federated training avoids raw data exposure, LDP ensures local feature desensitization, and blockchain-based audit logging provides immutable, transparent behavior tracking. Extensive experiments on real-world platforms—ranging from e-commerce sites to mobile social applications—demonstrate that our framework achieves superior success rates, adaptive behavior, and compliance scores compared to traditional, heuristic, and non-private baselines. The proposed system offers a practical and legally conscious solution for next-generation web crawling in dynamic, regulated ecosystems.