Is this lens worth it over the kit zoom?

Yes for low light and background blur. The f/1.8 aperture gathers far more light than a kit zoom and gives shallow depth of field, plus stabilization the kit lens lacks.

Does it work on full-frame Sony cameras?

It mounts on E-mount full-frame bodies but is designed for APS-C. Expect heavy vignetting and soft corners unless you shoot in crop mode.

How much stabilization does it add?

Optical SteadyShot compensates for hand shake, which helps in dim light and handheld video. On bodies with in-body stabilization the two work together.

Is the autofocus quiet enough for video?

Yes. Owners describe the focus motor as quiet and smooth, so it rarely shows up in recorded audio.

The lens comes with front and rear caps and a lens hood. A pouch is not included.

How does it compare with the Sony 35mm f/1.4?

The f/1.4 is a larger, heavier full-frame lens with a wider aperture and better edge performance. This f/1.8 is smaller, lighter and built for APS-C bodies.