Why can't SLR cameras take pictures with photographic lights?

There are many possibilities, 1, the shutter is too fast and the aperture is too small, resulting in underexposure and black picture.

There is something wrong with the shutter of the camera. Sometimes, in some cameras that have been used for a long time, when the shutter is at a high speed, for example, 500 seconds, a black screen appears before the shutter can move.

It is suggested that the landlord try automatic gear or A gear to eliminate the problem of taking pictures, and try the high-speed shutter of T gear. Is there a problem?