Navigating safely and efficiently in dense and heterogeneous traffic scenarios is challenging for autonomous vehicles (AVs) due to their inability to infer the behaviors or intentions of nearby drivers. In this work, we propose a distributed multi-agent reinforcement learning (MARL) algorithm with trajectory and intent prediction in dense and heterogeneous traffic scenarios. Our approach for intent-aware planning, iPLAN, allows agents to infer nearby drivers' intents solely from their local observations. We model two distinct incentives for agents' strategies: Behavioral incentives for agents' long-term planning based on their driving behavior or personality; Instant incentives for agents' short-term planning for collision avoidance based on the current traffic state. We design a two-stream inference module that allows agents to infer their opponents' incentives and incorporate their inferred information into decision-making. We perform experiments on two simulation environments, Non-Cooperative Navigation and Heterogeneous Highway. In Heterogeneous Highway, results show that, compared with centralized MARL baselines such as QMIX and MAPPO, our method yields a 4.0% and 35.7% higher episodic reward in mild and chaotic traffic, with 48.1% higher success rate and 80.6% longer survival time in chaotic traffic. We also compare with a decentralized baseline IPPO and demonstrate a higher episodic reward of 9.2% and 10.3% in mild traffic and chaotic traffic, 25.3% higher success rate, and 13.7% longer survival time.