Max Shutter speed
Panasonic LX100 can shoot continuously at max speed of
11.0 fps and has max shutter speed of
1/4000 sec. LX100 also has an electronic shutter which can shoot silently at max speed of
1/16000s. One thing to keep in mind is that electronic shutter may cause rolling shutter / jello effects, and also banding issues under artificial light on your images.
Flash
Unfortunately LX100 doesn't have a built-in flash but it has a flash shoe for mounting external flashes.
Focusing
Panasonic LX100 features a Contrast Detection autofocusing system. The AF system has 49 points to choose from.
Panasonic LX100 also features
Face detection AF where it intelligently detects the faces in the frame and locks the focus automatically.