Max Shutter speed
Sony RX100 III can shoot continuously at max speed of
10 fps and has max shutter speed of
1/2000 sec.
Flash
Unfortunately RX100 III doesn't have an external flash shoe so you are limited with the built-in flash.
One neat feature that we like about RX100 III's built-in flash has is that the flash head can be tilted upwards manually using your finger, which can be used to bounce the flash light and create a more pleasing lighting on your subject. It is not a very strong flash so the ceiling/wall or the surface you use for bouncing must be relatively close to the camera.
Focusing
Sony RX100 III features a Contrast Detection autofocusing system. The AF system has 25 points to choose from. Sony RX100 III also features
Face detection AF where it intelligently detects the faces in the frame and locks the focus automatically.