We report temporal coherence measurement of solid-target plasma-based soft X-ray laser (XRL) in amplified spontaneous emission (ASE) mode. By changing the XRL pumping angle, we generate lasing at two-times higher electron density than the routine condition. A relatively shorter coherence time at a higher pumping angle indicates a clear spectral signature of higher electron density in the gain region. We probe the amplification dynamics of XRL in routine, and high electron density conditions to confirm gain-duration reduction resulting from ionization gating in the latter case. We also present recent results on the seeding of a vortex beam carrying orbital angular momentum (OAM) in XRL plasma. A small part of the high topological charge extreme ultraviolet (EUV) vortex is injected in XRL. These preliminary results suggest that the vortex seed indeed can be efficiently amplified. In the end, we propose a pathway towards the seeding of the complete vortex beam and wavefront characterization of the amplified beam.