If the person indicated "left" passport data for the domain name and then engages in illegal activity on this domain as it can "calculate" public service?
You can not calculate, but to razdelyat domain in the pretrial order.
If you attract attention, the authorities make a request to the Registrar domain.
If the receptionist is not your personal data, confirmed by the scan of the passport (UNVERIFIED), the Registrar asks you for registration email. If in a short time they will not do this, the domain can be razdelyau. The Registrar may razdelyat domain and without asking you to confirm the data, if the domain was UNVERIFIED at the time of the request.
With regards to illegal activities, whether the "donation" (donation) players in exchange for virtual game values, illegal activity?
Yes, because you do not pay tax on income that is not registered as an entrepreneur/organization.
I assume you are hosting the server is already existing online game, and you are not the author/developer of the game client.
The bearer of a copyright can sue you in the court: copyright infringement, lost profits, intellectual property theft, illegal modification of the program.
In the UK, the condition of responsibility in respect of illegal entrepreneurship is major damage to citizens, organisations or the state or the generation of income in large size. Income in the large size or large damage is deemed or income in an amount exceeding one million five hundred thousand rubles.
But it is possible that the claim of copyright will include an assessment of your income provided by the plaintiff, looks like in terms of offensive responsibility.