1- if the breathing BECOMES adequate, assuming the avg rate 14-18bpm you may stop BVM ventilation and place them on an NRB. You dont want to force air into sombody breathing normally. Just because the breathing is labored or shallow does not nessicairly mean that breathing is "inadequate".
2 - according to the "book" you supposed to automatically suspect the patient fell or what not ie trauma, so go with the jaw thrust and last i checked as a BLS provider you should always place a BLS airway, NPA or OPA.
3 - suction, reposition the airway, BVM if the repositioning of the airway does not improve the patients respiratory rate.
Keep in mind this is all text book garbage. Its difficulty to treat a paper patient. wait till you hit the field if you havent yet, it will come much easier. Just keep in mind Lung sounds are very important and the pulse ox is an "aid" to your assessment, dont treat the pulse ox, treat the patient.