Hi, this adapter is for Canon EOS mount lens to Sony E NEX mount camera, we checked the sony a 7iii camera mount is E mount , this adapter can fit it , but you can reconfirme it , thanks.  

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

The longer Flange distance lens to the shorter Flange distance camera, then could use the infinity focus.
but if the shorter Flange distance lens to longer Flange distance camera, then could not use the infinity focus, you can focus on a limited distance.
the position of the infinity mark 【∞】of the telephoto lens or super telephoto lens is shifted slightly to the positive side to enable focus adjustment even when focus shift is caused due to temperature changes.The shift range is denoted by an L-shaped line, Be sure to check the focus through the viewfinder even when you shoot at infinity. 

yes, i had no problems with infinity focus with this adapter. the only FD mount lens i use anymore with my sony is a vivitar 20mm, and i pretty much only shoot infinity focus with it. 

No, this adapter is for the older manual focus Minolta Rokkor MC and MD lenses. If you want to autofocus and aperture control you will need the Sony LA-EA4. (the lower cost Sony LA-EA3 will electronically connect A mount lenses but you will have to manually focus.)