If family of two have health insurance, and one of them decide to use it for couple medical procedures will insurance policy premium go up?
No. The premiums will not go up for that. Usually health insurance is up for renewal once a year and the cost increases at that time, but not just because you use your policy. The cost of group health insurance where I work has had double digit increases in the premiums every year for 10 years now. The health insurance companies are out of control.
If you have insurance and need health care – go get the care you need.