Recent advancements in random distributed feedback Raman fiber lasers have promoted random Raman fiber lasers (RRFLs) as a novel laser source with significant progress. However, fully open cavity RRFLs suffer from suboptimal Stokes conversion efficiency and output power due to mode mismatch limitations. In this paper, we demonstrate the impact of end feedback and mode control on output Stokes wave characteristics. The random laser model incorporating multimode Raman interactions was established to theoretically simulate end feedback and output modal properties. Experimental studies were demonstrated through the construction of a fully open cavity RRFL. Higher end feedback reduces forward-propagating Stokes waves while amplifying backward-propagating light intensity. Transmission modes were effectively controlled through the design and optimization of tapered fiber. Consequently, 2081 W random Raman lasing was achieved in the fully open cavity RRFL. At maximum power, spectral purity exceeded 90%, representing the maximum output power reported for fully open cavity random lasers. This work provides important guidance for high-power laser generation and investigations of multimode nonlinear effects.