Intelligent reflecting surface (IRS) has gained great attention for its ability to create favorable propagation environments. However, the power consumption of conventional IRSs cannot be ignored due to the large number of reflecting elements and control circuits. To balance performance and power consumption, we previously proposed a heterogeneous-IRS (HE-IRS), a green IRS structure integrating dynamically tunable elements (DTEs) and statically tunable elements (STEs). Compared to conventional IRSs with only DTEs, the unique DTE-STE integrated structure introduces new challenges in both channel estimation and beamforming. In this paper, we investigate the channel estimation and beamforming problems in HE-IRS-assisted multi-user multiple-input multiple-output systems. Unlike the overall cascaded channel estimated in conventional IRSs, we show that the HE-IRS channel to be estimated is decomposed into a DTE-based cascaded channel and an STE-based equivalent channel. Leveraging it along with the inherent sparsity of DTE- and STE-based channels and manifold optimization, we propose an efficient channel estimation scheme. To address the rank mismatch problem in the imperfect channel sparsity information, a robust rank selection rule is developed. For beamforming, we propose an offline algorithm to optimize the STE phase shifts for wide beam coverage, and an online algorithm to optimize the BS precoder and the DTE phase shifts using the estimated HE-IRS channel. Simulation results show that the HE-IRS requires less pilot overhead than conventional IRSs with the same number of elements. With the proposed channel estimation and beamforming schemes, the green HE-IRS achieves competitive sum rate performance with significantly reduced power consumption.