econ難題xD

The free good is a term used in economics to describe a good that is not scarce. A free good is available in as great a quantity as desired with zero opportunity cost to society.
A good that is made available at zero price is not necessarily a free good. For example, a shop might give away its stock in its promotion, but producing these goods would still have required the use of scarce resources, so this would not be a free good in an economic sense.

As the production of medical services require giving up resources to produce other things, hence, they are not free goods.

Of course NOT. Nothing is free, and the government is paying out of the income derived from citizens, usally in form of taxes of all kinds, out of the pockets of the general public.