Yes, it fits Full-Frame Sony E-mount cameras (like the A7IV), but it will operate in 'APS-C Crop Mode,' resulting in a lower resolution image to avoid heavy vignetting.
Absolutely. The f/1.4 aperture allows for high shutter speeds in dark environments, and the stepping motor ensures silent autofocus that won't be picked up by microphones.
No, this lens does not have built-in Optical SteadyShot (OSS). It relies on the In-Body Image Stabilization (IBIS) found in cameras like the Sony a6600 or a6700.