As renewable energy and environmental protection gain prominence, community microgrid has become crucial for promoting resource sharing and improving energy efficiency. This paper presents a multi-stage optimization strategy of community microgrid considering fair allocation and risk management, utilizing the Vickrey-Clarke-Groves (VCG) mechanism and the glue value-at-risk (GlueVaR) method. The proposed strategy integrates carbon with the collective self-consumption (CSC) framework, using GlueVaR to manage uncertainties in photovoltaic (PV) power generation by balancing economic performance with extreme risk management. Compared with traditional risk management, the GlueVaR method offers a more comprehensive characterization of both tail risks and central tendency, enabling more robust decision-making under uncertainties. The VCG mechanism ensures accurate supply and demand reporting, thereby optimizing resource allocation. The proposed strategy aims to promote fair allocation, enhance community welfare, reduce carbon emissions, and optimize energy utilization. A distributed alternating direction method of multipliers (ADMM) algorithm is employed to improve the computational efficiency and preserve the privacy of community members, making the proposed strategy scalable to various community microgrid sizes. Case studies confirm that the proposed strategy significantly enhances community welfare, reduces carbon emissions, and strengthens system stability and security. Furthermore, by fostering fair and transparent transactions among members, the cohesion of the community is reinforced for long-term sustainability.