With regard to buying a car, you should probably buy it where you will register (and insure) it. I can't talk about all European countries, but in France you will not get insurance cover without a valid European driver licence. You might consider having a car registered and insured in the name of a relative in your partner's home country. You can then drive this car all over Europe with any driver licence as long as your status remains tourist. Health insurance is usually managed by the state and only available if you're a resident. As a tourist, you may buy a private insurance and ask for a European coverage. Apart from the price, I don't think there would be any issue with this.