If I need pain medications because I have acute pancreatitis, will I need to sign a pain contract?

Maybe. If you are in a hospitalized setting or need a small supply of narcotic meds, it is unlikely that you will need a contract, but it all depends on your prescribing physician. But if you need chronic pain meds, then it is highly likely to sign a contract.
Usually. Most doctors who prescribe controlled substances will require you to do so.
Depends. Lot of practitioners who do pain management have contracts as a part of standard protocol. Usually, a contract does imply that the practitioner knows the risks and benefits of prescribing pain medications.