No. Dilaudid has a short half life in the blood system and should be cleared out of your and your babies system by term unless you delivery within a day or two of your last dose.
Depends. States have different rules for testing newborns, and different responses to positive tests. If it was by prescription for an appropriate purpose, it might not be any kind of problem. Otherwise it could be. Your best bet is to discuss with your obstetrician or your pediatrician. The state is generally only involved if there is possibility of abuse or neglect of children. Report it yourself.