Layered materials exhibit different properties when they are thinned down to a few monolayers. Following the successful isolation of graphene in 2004, there has been a rapid increase in the number of studies focusing on other novel two dimensional (2D) materials such as hexagonal Boron Nitride (BN), transition metal dichalcogenides (TMDs), post transition metal chalcogenides (PTMCs), and in-plane anisotropic monolayers (Redichalcogenides and blackphosphorus). In addition to their electronic, optical, and magnetic properties, mechanical properties of 2D materials are of fundamental importance. Measurements of elastic constants of 2D materials are still challenging. Therefore, theoretical investigation of the mechanical properties is particularly important. Moreover, investigation of Raman spectra of these materials requires a through understanding of their vibrational properties. In these regards, we investigate the electronic, magnetic, and mechanical properties of some novel monolayer 2D materials (such as, auxetic pentagonal monolayers, flexible monolayers of holey graphene crystals, ultra-flexible monolayers of PTMCs, and in-plane anisotropic monolayers of ReS2 and blackphosphorus) by means of first-principles calculations based on density functional theory (DFT). In addition, tuning electronic properties of a van der Waals heterobilayer structure composed of monolayers of Mg(OH)2 and WS2 upon an external out-of-plane electric field is studied. The effect of biaxial strain on the vibrational properties of novel 2D materials is also studied through their off-resonant Raman activities. Our findings will be useful to clarify several issues related to the experiments of novel 2D materials.