Well, my parents didn't divorce, though we kids actually encouraged them to as they were so miserable together
How does the divorce law work in your country?
In the US I believe that all the states have no-fault divorce laws, or pretty close to that.  What it boils down to is that either party can initiate or insist on a divorce no matter what the cause of the breach.
In my country - Sweden, divorce law concerns the disslolution of child support, slimony, custody and the division of property
Well, here in the US that as well.  Division of property depends on whether it is a community property state which means roughly 50/50; child support for 0-24; alimony, not so much anymore.
How does the child support law work? Do parents make long term payment for the child?
Parents make payments based on their income, typically monthly.
Good to hear that. What is Medicare in the US? Is it a national social insurance program?
Medicare is only for those citizens who are 65 and older and who have contributed to the system through their work.