For intrauterine device, does nurse insert it or doctor?

Both. yAn IUD may be inserted bt a Doctor or Advanced Clinical Practioner (Certified Nurse Practioner, Certified Nirse Midwife, Physician Assistant) who is trained in IUD insertion.
Several options. An iud can be placed by a specialist who has been appropriately trained and does so safely. These include physicians, certified nurse midwives, certified physician assistants, & nurse practitioners. I've trained many mid-level providers and they perform an excellent job with this very effective form of birth control. I hope that helps.