We have studied effects of microscopic disorder (normal-state resistivity ρn) and dimensionality (film thickness t) on the vortex phase diagram at low temperature T on the basis of measurements of DC and AC complex resistivities for amorphous (a)- Mo x Si 1-x films with different ρn and t. For thick films (t=100 nm ) we have commonly observed the vortex-glass transition (VGT) down to low T~0.05Tc0 and high fields up to B~0.9Bc2(0), where Tc0 and Bc2(0) are the mean-field transition temperature and upper critical field at T=0, respectively. In the limit T=0, the VGT line Bg(T) is independent of T and extrapolates to a field below Bc2(0), indicative of the presence of a quantum-vortex-liquid (QVL) phase at T=0 in the regime Bg(0)<B<Bc2(0). We find that the width of the T=0 QVL phase, [Bc2(0)-Bg(0)]/Bc2(0), grows as the film becomes more resistive. This result is consistent with the view that the QVL phase is driven by strong quantum fluctuations, which are enhanced with increasing disorder. In the mixed state of the 6-nm-thick film, both the DC resistivity and vortex relaxation time follow the activated T dependence, suggestive of two-dimensional VGT.