Beam self-imaging of ultrashort pulses in nonlinear graded-index (GRIN) multimode optical fibers is of interest for many applications, including spatiotemporal mode-locking in fiber lasers. We obtained a new analytical description for the nonlinear evolution of a laser beam of arbitrary transverse shape propagating in a GRIN fiber. The longitudinal beam evolution could be directly visualized by means of femtosecond laser pulses, propagating in the anomalous or in the normal dispersion regime, leading to light scattering out of the fiber core via the emission of blue photo-luminescence. As the critical power for self-focusing is approached and even surpassed, a host of previously undisclosed nonlinear effects is revealed, including strong multiphoton absorption by oxygen-deficiency center defects and Germanium inclusions, splitting and shifting of the self-imaging period, filamentation, and conical emission of the guided light bullets. We discovered that nonlinear loss has a profound influence on the process of high-order spatiotemporal soliton fission. The beam energy carried by the fiber is clamped to a fixed value, and nonlinear bullet attractors with suppressed Raman frequency shift and fixed temporal duration are generated, leading to highly efficient frequency conversion of the input near-infrared femtosecond pulses into mid-infrared multimode solitons.