It is foreseeable the popularity of the mobile edge computing enabled infrastructure for wireless networks in the incoming fifth generation (5G) and future sixth generation (6G) wireless networks. Especially after a ‘hard’ disaster such as earthquakes or a ‘soft’ disaster such as COVID-19 pandemic, the existing telecommunication infrastructure, including wired and wireless networks, is often seriously compromised or with infectious disease risks and should-not-close-contact, thus cannot guarantee regular coverage and reliable communications services. These temporarily-missing communications capabilities are crucial to rescuers, health-carers, or affected or infected citizens as the responders need to effectively coordinate and communicate to minimize the loss of lives and property, where the 5G/6G mobile edge network helps. On the other hand, the federated machine learning (FML) methods have been newly developed to address the privacy leakage problems of the traditional machine learning held normally by one centralized organization, associated with the high risks of a single point of hacking. After detailing current state-of-the-art both in privacy-preserving, federated learning, and mobile edge communications networks for ‘hard’ and ‘soft’ disasters, we consider the main challenges that need to be faced. We envision a privacy-preserving federated learning enabled buses-and-drones based mobile edge infrastructure (ppFL-AidLife) for disaster or pandemic emergency communications. The ppFL-AidLife system aims at a rapidly deployable resilient network capable of supporting flexible, privacy-preserving and low-latency communications to serve large-scale disaster situations by utilizing the existing public transport networks, associated with drones to maximally extend their radio coverage to those hard-to-reach disasters or should-not-close-contact pandemic zones.