Young patient with obvious pain from recent injury and a probable cocaine problem. Urine clean. Do you give them a narcotic?

Probably ok. Depends on where pain is and what type of pain. If urine is clean and NSAID or other non-narcotic not effective for pain relief would not withhold appropriate pain relief due to history of Cocaine abuse.Just make sure you counsel patient on abuse potential, tolerance, etc, and abstinence from other drugs. Also limited quantity with close f/u.
Clear limits. I can't answer if the pain requires an opiate. However, i can say that from an addiction perspective, i tell patients that they must make it public (i.e. Tell spouses, their physicians and dentists) the planned duration of opiate use and pick the date to stop at the date of the prescription. After the date, they must be done with the opiate.
Closed monitor. If you suspect patient using cocaine, i'd be careful about prescribing narcotic medication for pain. I'd utilize other classes of pain killers like nsaids, anticonvulsants ... And maybe interventional procedures before prescribing narcotic medication. If narcotic medication is necessary, i'd monitor patient closely and utilize frequent drug screens.
Maybe... When you say "probable Cocaine problem, " are we talking about, they are likely to trade the prescription for something in the class of drug they prefer? I would say no to that. If it is a social user or reformed user, then i agree with our colleague above. If it has been days already since the injury, but he waited to see you, ask yourself why did he wait? Maybe he knew utox was coming?