Satellite communication is an important technology for the coverage of open country, and plays a vital role of link channel in remote Internet of Things (IoT). However, various kinds of IoT terminals may suffer from the limited battery capacity and computing capability. Therefore, this article proposes a new multiuser IoT system design, in which the satellite link is used to provide communication service for access points (AP), and allow terminals to download and upload data through APs. Then, the AP will exploit simultaneous wireless information and power transfer (SWIPT) and mobile edge computing (MEC) technologies to alleviate the deficiencies mentioned above. Moreover, the AP will equip with the full duplex (FD) and multi-input multi-output (MIMO) technologies to further improve the spectrum efficiency. Besides, a hybrid energy storage is assumed in the AP, i.e., the energy may come from power grid or renewable energy. Taking into account all issues above, we optimize the uplink achievable rate through jointly optimizing the CPU frequency, computation tasks, terminal transmitting power and the ratio of MEC task. In order to solve this optimization problem, we first decouple it into two sub-problems. For the first one, we can obtain the closed-form solution of CPU frequency. For the second one, we continue to decompose it into two non-convex problems, and then the iterative active-set method is used to solve these two problems. Numerical simulations demonstrate the effectiveness of the proposed design.