In this dissertation, we explore two outstanding questions in the formation and evolution of the large-scale structure. One question is that general relativistic corrections to the expansion rate of the universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this dissertation, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general in-homogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed 10-5 upper limit, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the universe needs to be further investigated with strong-field relativity.

As a second part of this dissertation, we have also studied the formation and evolution of Local-Group like poor galactic clusters. We analyze the star formation rate and examine the development of streaming flows toward the dominant galaxies of dwarf spheroidal protogalactic halos moving along the filamentary like structures in such a system. We show that this flow may impact the kinematics and star formation history in the halo and intergalactic medium.