[raxxorraxor]

You almost cannot. To find out what is relayed you would need to analyze the traffic your MacBook sends through your network adapter. This is pretty laborious since you need to filter a lot of noise to find respective apps sending data.

I would suggest to not use work devices for anything private. As for the MacBook not communicating you would need to look at your router or firewall. Or maybe Apple has specification about what constitutes it being off. MacBooks do use significant power while turned off but I don't know any details.