(Abridged). We present numerical simulations of isothermal, MHD, supersonic turbulence, designed to test various hypotheses frequently assumed in star formation(SF) theories. We consider three simulations, each with a different combination of physical size, rms sonic Mach number, and Jeans parameter, but chosen as to give the same value of the virial parameter and to conform with Larson's scaling relations. As in the non-magnetic case: we find no simultaneously subsonic and super-Jeans structures in our MHD simulations. We find that the fraction of small-scale super-Jeans structures increases when self gravity is turned on, and that the production of gravitationally unstable dense cores by turbulence alone is very low. This implies that self-gravity is in general necessary not only to induce the collapse of Jeans-unstable cores, but also to form them. We find that denser regions tend to have more negative values of the velocity divergence, implying a net inwards flow towards the regions' centers. We compare the results from our simulations with the predictions from the recent SF theories by Krumholz & McKee, Padoan & Nordlund, and Hennebelle & Chabrier, using the expressions recently provided by Federrath & Klessen. We find that none of these theories reproduces the dependence of the SFEff with Ms observed in our simulations in the MHD case. The SFEff predicted by the theories ranges between half and one order of magnitude larger than what we observe in the simulations in both the HD and the MHD cases. We conclude that the type of flow used in simulations like the ones presented here and assumed in recent SF theories, may not correctly represent the flow within actual clouds, and that theories that assume it does may be missing a fundamental aspect of the flow. We suggest that a more realistic regime may be that of hierarchical gravitational collapse.