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Here's an easy and safe thing you can do that might make you feel a bit more in control of your thoughts: drive around your town looking at the electrical poles, and notice how many of them have the same discs on top of them. Rationally, your neighbors can't all be targets of surveillance of some random company.
You have two possible choices:
- Technological (wireshark/MITM) to look at network traffic
- Sociological (trick your employer into admitting it)
Assuming that you aren't bothered about risking your job, then you could always do something that triggers your employer to act in a way that demonstrates that you are being monitored.
I don't have any great ideas of what you could do, but please make sure it is legal and ideally doesn't break your employment contract!
I am not one to turn away from a good conspiracy theory, so don't get me wrong. I just think you can see any patterns you want in the random noise of life. It is a strange set of symptoms your friend is experiencing, but why would they destroy your network, hampering you from being able to do work?