A friend of a friend’s house burned down due to a laptop overheating. His daughter left it running on the bed and the fluffy comforter blocked all the vents. This was maybe 15-20 years ago, and at the time, it wasn’t unheard of. I wouldn’t trust any device to turn itself off, especially lives are on the line.

You can. Just be aware you may need to select the output in your computer’s sound settings, because it may default to your monitor. It could do that(even if the monitor doesn’t have speakers, because a graphics card might register audio out through HDMI anyway.

Who provides the Internet and router? If it’s all your stuff and you didn’t authorize it, then it’s something shady. If all that is included in the rent, then it could be shady or innocuous.

I personally wouldn’t mention it to the landlord yet, because if it’s something shady, it will mysteriously disappear along with all tangible evidence.