Yes. Either Acetaminophen or Ibuprofen will treat a fever.
No. Fever of unknown origin, by definition, is unexplainable fever of prolonged period of over 3 weeks even after diagnostic interventions. No benefit is expected from otc medications.
No. If under age 6mo you should see your dr. If over 6mo, you may watch a low grade fever for about 2-3 days (<102), so long as it goes down with tylenol, (acetaminophen) your child looks good, and is drinking well. If not should be seen regardless of temp. If older, fevers past 5 days should be seen by a dr. To rule out treatable illnesses, such as strep throat, uti's, or other illnesses.