In this work, we propose and experimentally demonstrate an erbium-doped mode-locked fiber laser incorporating a single-mode fiber-graded-index multimode fiber-single-mode fiber (SMF-GIMF-SMF) structure. The SMF-GIMF-SMF segment serves as an artificial saturable absorber (SA), enabling hybrid mode-locking in combination with the nonlinear polarization rotation (NPR) mechanism. By tuning the intracavity polarization state and pump power, three representative mode-locking regimes are achieved: stable multi-wavelength output, wavelength-tunable conventional solitons, and soliton molecules (SMs). The soliton molecular dynamics are quantitatively analyzed by extracting temporal separations from spectral modulation fringes and autocorrelation traces. Tightly and loosely bound states are distinguished based on the ratio of pulse duration to soliton spacing. Experimental results confirm that the SMF-GIMF-SMF structure not only integrates filtering and saturable absorption functionalities but also offers significant advantages for achieving multi-wavelength mode-locking and soliton molecule formation. These findings provide a promising experimental foundation for the development of low-cost, highly stable, and multifunctional ultrafast fiber lasers.