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. 

Could you please update us your full Minolta lens model ?as Minolta has MD MC and AF mount, K&F Concept MD-M4/3 is suitable for: Lens: Minolta MD MC Mount lens(not for Minolta AF mount: KF06.157) Camera: Micro 4/3 (MFT) mount mirrorless camera like Olympus PEN, OM-D series, Panasonic Lumix DMC-G1, G2, G3, G10, GX1, GH1, GH2, GF1, GF2, GF3, GF5, GH4, Panasonic AG-AF100 Mirrorless Digital Cameras, Black Magic Pocket Cinema Camera (BMPCC) 

Yes 

As far as I know it will, I was not informed that Sony had changed the size of the lens mount on the new sony’s A7 models , that would be counter productive to any person owning a Sony lens! 

Yes. I bought this to mount my Canon 50mm FD to my Sony a6000. It works awesome!