How is traffic monitored when I start a client? Don't I need to download/upload something to get monitored? Is the monitoring connected to trackers I download from or ISP monitored?
"[...] with a heavy fine."
Was it a fine or some kind of fee? ("Abmahngebühr")
As for the traffic monitoring, indeed, I'd imagine it to be honeypot tracker where all content/traffic is visible rather than something installed on the ISP side.
There are companies who join the download swarm and register all other downloading parties. That's very easy with bittorrent, since the protocol is (originally) designed for fast download sharing without any regard to anonymity or pseudonymity.[1] The process is not reliable for providing evidence of copyright infringement, though, and the German system mostly works by scare tactics of lawyers - many people don't want to risk a lawsuit even if they could win it.
[1] https://torrentfreak.com/thousands-of-spies-are-watching-tra...
They sent some awfully scary letters for what amounts to legally obtaining an ISO file.
In other words, such things are considered low-hanging fruit by these companies. Just throw it out there and see what sticks.
Though that only tells you the RIPE member for it.
They might have still leased the IP elsewhere (which is totally informal, if you operate a IP range all you need is a letter saying you can do it with the owner's signature)
Insane, you can get a good VPN from TorGuard, PIA or NordVPN for 10x less than half of an episode!