1, orthodontics, medical insurance card is definitely ok, the dentist will find a way.
2. Large hospitals are expensive. I suggest you find a dental clinic with good reputation, good technology and many years of operation. There are many private dental clinics like Qingdao now, so it's best to go to a clinic near your home. You can also ask the doctor to have a look at your teeth and ask how much it costs. You said that some people have time to fix it.