it could work with a nikon f-mount (d3300) to sony e-mount( a7iii). 

Yes, it will fit any Sony e mount body, either full frame (a7..., a9...), or aps-c (like a6500, etc) 

The V50x comes with a skeleton case with a slotted rear door replacement, but there is no opening to allow plugging in an external mic. As a note, the sound recording, even while in the completely waterproof case, is better than I had expected. If you're not worried about moisture, there is a threaded tripod mount on the bottom of the camera and an adapter that will allow you mount the camera without using the case. 

Yes, the A7III is an E Mount lens mount. 

Yes, Sony A6000 is with E mount, this item will be suitable for your camera