This study employs the water-gas-shift membrane reactor and multi-effect distillation with thermal vapor compression technologies to facilitate low-energy carbon capture and large-scale freshwater production in gasifier-solid oxide fuel cell (SOFC) systems. The supercritical CO2 Brayton cycle and double-effect absorption refrigeration cycle are introduced to achieve waste heat cascade recovery. This work expands the fuel selection to 12 biomasses to explore the fuel adaptability and application scenarios of the system, and selects four representative cases to reveal their thermodynamic and economic attributes. The base scheme produces 21,635 ton/year freshwater and 1333 ton/year CO2, and achieves energy and exergy efficiencies of 70.68 % and 30.60 % with total cost rate of 23.21 $/h and levelized cost of products of 43.55 $/GJ. The gasifier and SOFC effort contributes to over 60 % of total irreversibility. Larch wood is preferred in resource-rich regions while wood residue, switch grass and wood chip are also prioritized; rice straw, rice husk, cotton stem and algal biomass are suitable for water-scarce areas. As key parameters change, Case-II consistently excels in power output, efficiencies and economic aspects, but lags in cooling capacity compared with other cases. This work provides a reference for low-carbon transition in the energy sector and large-scale freshwater production.