I use it on the Sony Alpha 6000 with a manual FD 50mm. AF and aperture transmission are not an issue here. Actually, the adapter only keeps the lens at the right distance in front of the sensor. This works great and I think it will be the same with the Alpha 7III. 

Better is the sigma adapter...don't hesitate 

No, the maximum compatible filter size is 82mm 

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

The adapter will mount the lens and you will be able to use it manually. However, my copy of the adapter does not allow the lens to be fully mounted all the way until it clicks into place. It doesn't quite make it, but it's still very solidly mounted. Also, the manual aperture linkage doesn't work properly (on my copy, at least) so exposure is controlled only by shutter speed and/or ISO. You will be able to manually focus and zoom the lens but no VR, of course. It will be a frustrating experience. Instead, get a 14-140 Panasonic zoom if you can afford it!