Controlling the basic properties of light such as polarization, angular momentum, and speed through various optical media leads to interesting phenomena in various fields such as quantum optics, photonics, plasmonics, and quantum information technology. Few of the phenomenon include, for instance, light storage, ultra-slow and ultra-fast propagation, optical transparency, and quantum entanglement via quantum coherence or superposition. The understanding of these phenomenon of milestone implications paved the way for the invention of novel classical and quantum technology. In this article, we present detailed theoretical and numerical demonstration on the dispersion-dependent phenomenon of slow and fast light, optically induced transparency, and photon drag. For this, we employ a three-level scheme of an ensemble of GaAs\AlGaAs double quantum dot molecule in cascade configuration. In particular, by tuning the medium dispersion we predict interesting interplay between ultra-slow and ultra-fast light propagation with vanishing, infinite, ultra-positive and ultra-negative group velocities, and optical-assisted quantum transparency. The quantum coherence of the dressed states modifies considerably the optical properties of the system in view of dispersion, absorption, electron energy loss, transmission, and photon drag. An interesting interplay between ultra-slow to ultra-fast propagation is found by tuning various optical parameters. The calculated superluminal value of group velocity is ±6×10^11 m/s. We also predict light propagation at vanishing and infinite group velocity. The calculated light drag is ±6×10^(-6) rad/m.