This paper investigates the hybrid interaction dynamics of diverse localized waves in the focusing complex short pulse equation, a key model for ultrashort pulse propagation in optical fibers. By developing a generalized \((p,N-p)\) -fold Darboux transformation based on the Lax pair, we analytically construct semi-rational soliton solutions of smooth, cuspon and loop types, all of which are governed by a single spectral parameter. More significantly, by precisely controlling two spectral parameters, we report for the first time nine distinct hybrid interaction structures among smooth, cuspon, and loop rogue waves and their respective periodic wave counterparts. The spatial positions and shapes of these localized waves can be effectively manipulated by tuning key parameters, and their structures and dynamical evolution are clearly visualized through graphical illustrations. These results not only deepen the understanding of hybrid wave structures but also provide new theoretical insights into the propagation mechanisms of ultrashort optical pulses in nonlinear media.
