Recent advances in experimental and computational methods have opened up new directions in graphene fundamental studies. In addition to understanding the basic properties of this material and its quasi-one dimensional structures, significant efforts are devoted to describing their long ranged dispersive interactions. Other two-dimensional materials, such as silicene, germanene, and transition metal dichalcogenides, are also being investigated aiming at finding complementary to graphene systems with other "wonder" properties. The focus of this work is to utilize first principles simulations methods to build our basic knowledge of structure-interaction relations in two-dimensional materials and design their properties. In particular, mechanical folding and extended defects in zigzag and armchair graphene nanoribbons can be used to modulate their electronic and spin polarization characteristics and achieve different stacking patterns. Our simulations concerning zigzag silicene nanoribbons show width-dependent antiferromagnetic-ferromagnetic transitions unlike the case of zigzag graphene nanoribbons, which are always antiferromagnetic. Heterostructures, build by stacking graphene, silicene, and MoS$_2$, are also investigated. It is found that hybridization alters the electronic properties of the individual layers and new flexural and breathing phonon modes display unique behaviors in the heterostructure compositions. Anchored to SiC substrate graphene nanoribbons are also proposed as possible systems to be used in graphene electronics. Our findings are of importance not only for fundamental science, but they could also be used for future experimental developments.