With the aroused attentions on promoting renewable energy and the increasing penetration of distributed energy resources (DER) and the electric vehicles (EVs), providing the energy management tools efficiently for operating DERs and EVs grid-friendly and attracting customers to involve the management have become the important issues. An extensive cloud-based framework is firstly proposed to provide the energy management as a service (EMaaS) for customers (i.e., DERs owners). Customers who are involved in the same EMaaS form the ``community" to trade their produced renewable energy virtually among others. By facilitating the DERs, storage systems, and the customers' trading choices within the same community, incentives are maximized as the global cost is minimized and renewable energy integration is enhanced as the renewable energy consumption is stabilized by the proposed EMaaS for each community. To further attract customers not only involve in controlling their consumption patterns but also participate actively, and operate EVs and DERs within the community grid-friendly, the fair demand response with the EV is secondly realized for the cloud-based energy management service (F-DREV). The choices of electricity usage and trading are combined to further minimize the global cost for each community while distributing incentives fairly to the individual customer. The cross-community interaction (XCI) and adjustment (XCI) are thirdly proposed for the cloud-based energy management. XCI minimizes the global costs for the collaborated communities and is performed in the distributed fashion to overcome the privacy concern and the difficulty for handling the large-scale data. XCA enhances the efficiency of XCI under uncertainty, where the overwhelmed data exchanging and the computations can be significantly reduced.