Results of the numerical study on the initial formation stages of low-mass protostellar systems leading to single, binary, triplet, and quadruple protostar systems formation are reported here. In addition to these various types of protostellar objects we also investigate the overall structure formation that takes place within collapsing molecular cores that yield during the course of evolution the spiral structure formation, ring formation, and bar formation under various initial conditions chosen for a rotating solar mass cloud of molecular hydrogen to mimic the states prevailing in star formation regions in our Milky Way galaxy. There have been three key parameters belonging to the initial star forming conditions whose effects on the overall outcome of protostallar systems have been examined. These parameters are the initial thermal state of the prestellar core, the amplitude of azimuthal density perturbation introduced in initially uniform density state of the core, and the impact of the critical density which governs the transition from isothermal to adiabatic thermodynamic behavior of the collapsing core. For protostellar binaries, the separation is determined as a function of the initial thermal state of the core by varying its initial temperature. For this purpose a slightly modified version of the Burkert and Bodenheimer collapse test is taken into consideration. We find that the result is fairly sensitive to both the initial thermal state of the cloud and the initial azimuthal density perturbation’s amplitude A. For A=10 %, variations of only 1 unit Kelvin below 10 K causes a change of up to 100 AU in protobinary separation, while for this small amplitude of perturbation the initial temperatures above 10 K result a single low-mass fragment, instead of a binary, that does not reach even near to the protostellar densities. However, protostellar binaries, do appear if the amplitude of perturbation is enhanced from 10 % to 25 %. A star forming hydrogen gas is normally considered to be initially at 10 K. For structural formation study, we have explored that an oscillation around this normally considered value can be influential in determining the fate of a collapsing gas as it evolves in its structural properties that may lead to formation of proto-stars. We examined the initial range of temperature of star forming gas between 8 K to 12 K and tried to compare the emerging physical properties within the early phase of formation of protostellar system. According to our findings the spiral structures are likely to appear in a strongly perturbed molecular cores that commence their phase of collapse from temperatures lesser than 10 K. However, cores with initial temperatures more than 10 K potentially develop, instead of spiral, a ring structure which afterwards experiences the clumps formation. It is possible to observe a transition from spiral to ring instability at a typical initial core temperature of 10 K. Similarly, while investigating the effects of critical density variations on the evolution of protostellar systems, we find that the critical density affects the structural evolution of the envelope of gas, also the dimension of emerging rotating disk structures during collapse too get affected as well as the number of fragments appearing from the concluding fragmentation of the disks. It is suggested that this mechanism has the potential to give birth to young protostellar objects that may eventually constitute systems of bound multiple protostars. The entire numerical experiment is conducted by using 250025 SPH particles to construct virtually the geometry of each molecular core investigated here.