@santiago
We pay 150-200TWD for the doctor's visit, but almost all of the medicine is free. Some surgical procedures require a fee if it's not deemed entirely necessary. For example, my wife had an endoscopy a long time ago, and we had to pay for the anesthesia (because the procedure can be done without it, it's just uncomfortable). Another example, I had surgery a couple of years ago, but we upgraded my room to a 2-person room (standard is 4), and I had to pay for the blood salvage machine (standard is blood transfusion).
I'm less sure about education here because we don't have kids. Elementary school is free and the gov't has free junior and senior high schools (there may be some fees involved for these latter two for books and materials, but I'm not sure), and there are private schools, too. Almost everyone here goes to university. That's not a joke. Those that don't go to university do so by choice, not because of financial problems. I believe it's subsidized, but I'm not sure how much. It isn't financially burdensome, though.