In a first stage, I do not have to convince any court. I have to file a lawsuit.
No, you have to convince a court that they have jurisdiction to hear your lawsuit.
You have to apply to them to be allowed to serve your filing out of their jurisdiction.
In Europe, you can do this basically with a simple letter sent to your local police station.
At least in the UK, that is simply not true.
The police would have no interest in your civil complain against KNC, they investigate criminal offenses.
But you are right: They claim in their TandC that you have to make a business out of the miner. However, this is even better: So private persons can claim that they were in a state of "Eigenschaftsirrtum".
You can claim all you want, you still have to file a lawsuit, get agreement to serve out of state, and convince the court to accept jurisdiction.
Furthermore: If you want to set up a business as an individual, you still are protected as a consumer.
I don't think that is true.
In Austria, Germany and Switzerland, you don't have to go to a court. You go to the next police station, tell them what happened (best, you write it down and name the claims, cops don't like to much work). That's it. No court involved. Then it goes to the magistrate judge. Still no court involved. If you write your complaint well enough and back it up with evidence, it is up to him to decide what to do next. He can issue a request for an arrest warrant. Still no court involved. This all is for a criminal complaint, not a civil one.
And regarding the individual: You can set up a company without capital, i.e. use the miner as capital. As long as the miner is not delivered, the company is not existing, thus, you still are a private person protected by consumer laws. If you ask for a refund, you stop being a possible business, i.e. you are again a consumer who's assets are not sent back in time.