how does live view work?
It depends on the camera. With SLR's, yes, the shutter opens. AF is now mostly done off the sensor (CDAF) in live mode. The Sony translucents are different as the mirror never moves and PDAF is always active.
In mirrorless cameras, there is only live view and CDAF.
Overheating of the sensor, especially the larger APS sensors is a problem. Cameras will shut down if the sensor starts to overheat, and it does.
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