Health care

I am not totally understanding exactly what you are asking but I do know that immigration asks that you have health insurance for at least one year before you are considered to enroll in the national Health program in Hungary.
I do not know your immigration status so these details may be different for you then what I had to do.
I am married to a Hungarian citizen who has returned to Hungary for retirement. Even my husband who is a Hungarian citizen by birth had to pay into the system for one year before he was allowed to use his health card for anything other then an emergency.
I used Generalli insurance co. for my first year in Hungary for health coverage. They have a rate for students which I was able to also be covered under. It was reasonable for the first year of coverage. This was 2 years ago, things may of changed since then. I was charged approx. $250. for the year with Generalli insurance co.
We now pay out of pocket monthly for national health coverage at the going rate of around 6,800 per month each.
Seems cheap enough but with all the tipping involved with seeing any doctor it can be expensive to even get a quick office visit.
Tipping is not required of course but if you plan on ever returning to the same doctor again my advice would be to tip for services. We usually tip between 2,000 to 5,000 each per visit and for a specialist we tip at least 10,000 per visit.
For surgery we tip depending on how long the procedure took, from one hour to two or more, Tipping nursing staff, orderlies etc. can add up to almost the cost of just paying out of pocket for the entire operation and having a private room.
If we do not get decent service with tipping we skip tipping to every few visits and for good service we tip at every visit.
My husbands father didn't tip his dentist one time and he got the wrong tooth pulled out, just saying tipping somehow improves the doctors skills.