dont't try - its going to burn the sensor, as it will overrun it's thermal capacity. this is why there is the 30 mins limit in the first place; you'll see a marked raise in noise after 10 mins or so any way
The limit is only for tax purposes. One guy at my work uses Sony DSLR as webcam and it works just fine and we are staying with cams/mics on for hours at a time (pair programming)
Indeed. My A7ii uses a very similar sensor to some Nikon cameras, and the sensor is literally always on, because the camera lacks an optical viewfinder. While the noise for very long exposures is negatively affected by the temperature of the sensor if left on too long without being allowed to cool down, the camera is made for having the sensor on for hours and hours every day without issue, and the Nikon sensors aren't any different.
Whats most likely to break, however, is the shutter mechanism. But even that isn't affected here.