Max Shutter speed
Fujifilm X-T1 can shoot continuously at max speed of
8 fps and has max shutter speed of
1/4000 sec. X-T1 also has an electronic shutter which can shoot silently at max speed of
1/32000s. 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 X-T1 doesn't have a built-in flash but it has a flash shoe for mounting external flashes.
Built-in Flash of Fujifilm X-T1
Focusing
Fujifilm X-T1 features both Contrast Detection and Phase Detection autofocus (AF) systems which ensures speed and accuracy of focusing in most situations.
Fujifilm X-T1 also features
Face detection AF where it intelligently detects the faces in the frame and locks the focus automatically.