This Thesis is mainly devoted to the exploration of the structural disorder and magnetic order in two-dimensional crystals by means of first-principles methodologies. Firstly, we present a comparative study of defect formation in the semiconducting 2H and semi-metallic 1T' phases of MoS2, the most representative member of transition metal dichalcogenides. We assess the thermodynamic stability of a broad set of point defects, along with their effect on the electronic structure and magnetic properties. We further investigate the response of 1T'-MoS2 to the electron beam irradiation. The energy range of the electron beam which is necessary to conduct sample imaging without inducing knock-on damage, as well as to intentionally create vacancy defects in 1T'-MoS2 is dicussed. Next, we show how native defects can be exploited to induce magnetism in otherwise non-magnetic ultrathin PtSe2 by providing a theoretical model which explains magneto-resistance measurements. We reveal an antiferro- and ferro-magnetic ordering in semiconducting mono- and bi-layers, respectively, together with a layer-dependent RKKY interaction in thicker metallic films. Secondly, we focus on magnetic interactions in monolayer CrI3 by determining the strength of both intra- and inter-site magnetic exchange interactions. We find that inter-site exchange interactions are primarily dominated by the ferromagnetic isotropic Heisenberg coupling, being inter-site anisotropic terms substantially weaker. Also, this system features a single-ion anisotropy pointing along the out-of-plane direction. Then, we show that Heisenberg exchange interactions can be effectively modulated through mild lattice deformations. In fact, depending on the magnitude and direction along which the strain is exerted, monolayer CrI3 undergoes a transition from the ferromagnetic phase to either Néel antiferromagnetic or ferrimagnetic phase. Additionally, we briefly examine the role point defects on monolayer CrI3, and point out an interplay between lattice disorder and local magnetic moments in this system. Thirdly, we revisit two fundamental yet poorly understood problems in physical chemistry. These include the hydration dynamics of the excess electrons in liquid water, a species relevant to many biological and chemical processes, and the nature of double bonds between higher main group elements, with a particular emphasis on the comparison between the properties of C=C vs Si=Si, an issue which is crucial to understand the structural dissimilarities between graphene and silicene.