No, the UK can't ask for an income statement - the rules only require that people can prove they have enough money to live on. No, they don't have to pay tax - that only happens if they have income. No, this isn't limited to three months - that's only the point where they have to prove they can support themselves in order to remain. And whilst most of the EU doesn't use the US model of insurance, the state-run healthcare in the other EU states is generally set up as a state-operated "insurer" which you have to pay into for coverage. The UK is pretty much unique in funding healthcare from taxes and giving access to all residents for no extra charge.