The Bi2Se3 with hexagonal crystal structure has been widely studied over the last decade as an active candidate of the 3D topological insulator (TIs) due to its simple band structure, single Dirac cone at the Γ point, and spin-momentum locked surface states. In most cases, the surface properties of Bi2Se3 get hindered due to high carrier density and anti-site defects. However, the Bi2Se3 in the form of nanostructure provides an opportunity to enhance the surface properties and overcome the bulk contribution as the nanostructured Bi2Se3 has a large surface-to-volume ratio. In this work, hexagonal-shaped nanocrystals of Bi2Se3 have been prepared by the chemical hot-injection method using non-toxic solvents. These nanocrystals dispersed between Ag contacts exhibit thermally activated behavior with Poole-Frenkel conduction due to electron trapping/de-trapping barriers between the nanocrystals. These nanocrystals exhibit band transition energy around 0.66 eV, which is more than the reported bulk values. The band structure was calculated using the Density Functional Theory (DFT) to understand the origin of expanded bandgap of nanostructured Bi2Se3. The calculations indicate that the larger surface area with hexagonal symmetry rather than the surface-to-volume ratio leads to the expanded band gap due to the interplay between van der Waals and covalent interactions in the Bi2Se3. The band structures of (0001) surface of Bi2Se3 indicate the shifting of Dirac point towards or away from Fermi level by the application of strain on the Bi2Se3 slab. In addition, the presence of different asymmetric/non-stoichiometric termination of atomic layers on the top quintuple layer of the Bi2Se3 slab drastically changes the band structure of (0001) surface of Bi2Se3, which leads to the formation of topological dangling bond states. The spin texture of the Bi2Se3 calculated at the valance band maximum shows the variation of spin density and orientation under strain, which confirms the strain's tuning of spin-orbit coupling strength. Our calculations on spin texture and band structure suggest that Bi2Se3 can be a model system for the study of various topological phenomena and the design of artificial topological insulators for technological applications.