Both stationary and time-dependent regimes of operation, instabilities, and phase squeezing are investigated in the off-resonant two-photon correlated-spontaneous-emission laser by numerical calculation. Initial atomic coherence plays an essential role in lasing without population inversion, phase locking, and phase noise squeezing in the system. Under certain conditions, in the inverted and noninverted regimes alike, the output intensity exhibits bistable behaviors against the initial atomic coherence. Depending on the parameters, the whole or a portion of the upper or lower branch gives stable operations. In the inverted regime, even tristable behavior can be found in a narrow range of parameters. The field evolution and dynamics are studied. Furthermore, phase noise reduction near bistable areas is also investigated. In addition to the lower branch, where from previous studies, it has been known to exist, phase squeezing is also found on the upper branch both with and without population inversion, thus generating a bright source of phase noise squeezed light.