Addiction Prevention and Responsible Opioid Practices Act This bill addresses substance use and mental health related to opiods, including by imposing an excise tax on opioids; modifying controlled substances regulations, prescription drug monitoring programs (PDMPs), and health insurance coverage; and requiring other activities. Specifically, the bill (1) establishes federal licensure requirements for pharmaceutical representatives who market opioids, (2) requires certain training and PDMP participation as conditions for controlled substance registration, and (3) withdraws regulatory approval for opioids with ultra-high doses. In addition, as a condition for receiving certain grants, recipients must, for example, mandate the use of PDMPs in specified ways and increase data-sharing. Additionally, to meet certain certification standards, health information technology must be interoperable with PDMPs. Additionally, the Centers for Medicare & Medicaid Services (CMS) must reimburse mental health services provided through telehealth under Medicare and develop a web-based tool to compare opioid prescribing in state Medicaid programs. The bill also creates grants to support compliance with requirements to provide parity in insurance coverage for mental health and substance use disorder services. The Government Accountability Office must study health care coverage and reimbursements for substance use disorder treatments. Furthermore, the Department of Health and Human Services and the CMS must develop quality measures and guidelines for treatment of non-fatal overdoses, and the Department of Justice must operate a drug take-back program. The National Academies of Sciences, Engineering, and Medicine and medical and dental schools must also report on Medicare coverage of non-opioid treatment for back pain and educational courses on pain management and opioid prescribing practices, respectively.