Is this lens worth it over the Sony 18-135mm?

If size is the priority, yes: it is far smaller and lighter. The 18-135mm gives much more reach and better sharpness, so pick that one if you shoot distant subjects more than you carry the camera.

Does it work on full-frame Sony cameras?

It is an APS-C E-mount lens. On a full-frame body it works only in crop mode, which throws away most of the sensor.

How good is the stabilization?

Optical SteadyShot helps with handheld stills and video, and it pairs with in-body stabilization on bodies that have it. It does not replace a fast aperture in very low light.

Is the power zoom good for video?

Yes. The motorized zoom gives smooth, even transitions that are hard to match by hand, and the autofocus motor is quiet enough not to be picked up.

What comes in the box?

This is a white-box version, so expect the lens and caps rather than the full retail kit. Check the listing for the exact included accessories.

Is it sharp enough for everyday photos?

Centers are decent stopped down, and in-camera correction fixes most distortion. Corners stay soft at the wide end, so it is not the lens for large prints of wide scenes.