This thesis presents a comprehensive study of the least explored aspects behind the underlying physics of gamma-ray bursts (GRBs), with a specific focus on three major ones, utilising multiband space/ground-based data, including those obtained from the 3.6m DOT, 1.3m DFOT, and others. To study the nature of the underlying physical mechanisms and the central engine powering the emission from such highly energetic stellar explosions, the first project presents a statistical analysis of the features observed in the light curves of 200 GRBs detected by Swift-UVOT/XRT/BAT between 2005 and 2018. The second project explores the nature of ultra-long GRBs, including the BOAT (GRB 221009A), which lasts 100 to 1000 times longer than typical GRBs, to better understand their progenitors, central engines, and the role of their environment in sustaining such prolonged emissions. The third project studies the prompt and afterglow emission properties of a rare sample of TeV-detected GRBs (GRB 201015A, 201216C, GRB 221009A, etc.) to investigate whether their behaviour differs from, or is consistent with, that of typical GRBs. Together, these three projects have added value towards our understanding of the physics behind these enigmatic sources, particularly regarding the nature of the underlying physical mechanisms, the central engine, and their environments.