I think government must give everyone their insurances equally. We shouldn't let private health insurances. What do you think about? Do you have any ideas?

I don't see how you can possibly have health insurance - you would need private healthcare infrastructure for that to work but something like healthcare for an initial colony of 10,000 (is it 10,000) would have to be centrally funded and in all likelihood would be quite rudimentary compared to Earth and would rely on a lot of remote assistance, for instance a colony that small would not sustain the full range of specialists you would expect in a even a small general hospital. 

Asgardia wouldn't want to pay a Gastroenterologist to sit around twiddling their thumbs doing nothing for most of the day and you wouldn't want to go and have a procedure done by a Gatroenterologist that doesn't do enough procedures to remain competent.