Does it makes sense that I can only see a pain doctor once a year? The other times I need to see the nurse practitioner. Never heard of this.

Sometimes. In some pain practices the md does the initial evaluation and when a patient is fairly stable an np will do follow-up visits. The np should refer new questions or issues back to the physician who should be available on premises.
No. Whay to see pain doctor only once a year......If you have stable and controlled pain then just see your pcp. I am sure insurance company also agrees with me!
Could be. The current medical trend is incorporation of np more. Talk with them if you feel you need other issues addressed by physician.