After successful isolation of graphene in 2004, it was found that the layered materials showed different properties when diluted to the monolayer. The layer dependent structural, electronic and vibrational properties of the 1T phase of two dimensional (2D) platinum diselenide are investigated by means of state-of-the-art first-principles calculations. In addition ultra-thin two-dimensional Janus type platinum dichalcogenide crystals formed by two different atoms at opposite surfaces are investigated by performing state-of-the-art density functional theory calculations. While all Janus structures are indirect band gap semiconductors as their binary analogs, their Raman spectra show distinctive features that stem from broken out-of-plane symmetry. Moreover, it was shown that vertically stacked van der Waals heterostructures of binary and ternary (Janus) platinum dichalcogenides offer wide-range electronic features by forming bilayer heterojunctions of type-I, type-II and type-III. On the other hands, Ab initio calculations are performed in order to investigate the structural, vibrational, electronic, and piezoelectric properties of both bare TaS2 and its functionalized structures. Furthermore, the elastic and piezoelectric properties of TaS2 and its derivatives are analyzed. It is revealed that the in-plane piezoelectricity of TaS2 can be enhanced via one-surface fluorination while an additional degree of freedom for the piezoelectricity can be added in all Janus structures due to the broken out-of-plane symmetry. This thesis provides some important results understanding of thickness and functionalization dependent mechanics, vibrational, electronic properties of 2D materials.