Charge carrier dynamics essentially determines the performance of various optoelectronic applications of colloidal semiconductor nanocrystals. Among them, two-dimensional nanoplatelets provide new adjustment freedom for their unique core/crown heterostructures. Herein, we demonstrate that by fine-tuning the core size and the lateral quantum confinement, the charge carrier transfer rate from the crown to the core can be varied by one order of magnitude in CdSe/CdSeS core/alloy-crown nanoplatelets. In addition, the transfer can be affected by a carrier blocking mechanism, i.e., the filled carriers hinder further possible transfer. Furthermore, we found that the biexciton interaction is oppositely affected by quantum confinement and electron delocalization, resulting in a non-monotonic variation of the biexciton binding energy with the emission wavelength. This work provides new observations and insights into the charge carrier transfer dynamics and exciton interactions in colloidal nanoplatelets and will promote their further applications in lasing, display, sensing, etc.