When must FAA reply to my letter?
The FAA publication "MEDICAL FACTS FOR PILOTS" Publication #OK-06-002 states the time periods shown below. I don't know of any rule that mandates a response in any specific time period.

We will respond to your request for duplicate medical certificates within 3 working days of receipt.

We will respond to your request for full review of medical records within 30 working days of receipt of all the necessary records and testing.