Horse's mouth. Always best to get it straight from the horse's mouth. Call your health insurance and check out your coverage.
Yes. Check with your insurance to know specific doctors covered. Call the number on back of your card.
Pain management. Pain management is a sub-specialty of medicine. It's covered by all insurances.
Probably. The only way to know for certain is to check with your insurance company. They may require a referral from your primary care physician, or that you only see specific pain specialists.