Hi, Just wanted to interject that the Sony 24-70mm f2.8 GM does not have OSS so it relies on the body for any stabilization. take care, Rick 

Center is just a focusing zone, lock on is set in tracking sensitivity https://helpguide.sony.net/ilc/1830/v1/en/contents/TP0002384077.html?search=Focus lock

Did the firmware update delete it?

I'd try a factory settings reset and see if the issue persists. Not sure which setting might cause this behaviour. It would be less annoying if the 16-50 lens collapsed immediately after switching the camera off but alas, it waits with collapsing until the camera is completely finished with whatever it's doing. Hot pixels occur in cameras of all ages from all brands. I've occasionally spotted a hot pixel in my camera, but after a hot pixel mapping routine the issue was totally gone. Wouldn't worry about this as it's adequately dealt with in Sony cameras.

Hi taonight, this is frustrating! Sony SEL200600G with A6000 is not a general problem. I use this setup as well and don't see any abnormal patterns (even if I push the exposure to the maximum and see almost only noise). I also use the full-frame Sony A7R with the SEL200600G lens and I don't see any patterns. The picture shows one of my first asotrophotos with this setup - also the Andromeda-Galaxie M42, 28x40s F5.6 ISO-800 600mm. I would recommend trying a different stacking software or maybe a different RAW converter. Do you have the possibility to test the lens with another Sony E-mount camera?