Nursing management of headache would include:

Choice A: Respiratory status is the first priority, as it can affect the oxygenation and perfusion of the brain and other vital organs. The nurse should assess the rate, rhythm, depth, and quality of breathing, as well as the use of accessory muscles, chest expansion, and lung sounds.

Choice B: Alertness is not the first priority, but rather a component of the level of consciousness. The nurse should assess the patient's ability to open their eyes spontaneously or in response to stimuli, as well as their orientation to person, place, time, and situation.

Choice C: Motor response is not the first priority, but rather a component of the level of consciousness. The nurse should assess the patient's ability to move their limbs voluntarily or in response to stimuli, as well as their muscle strength, tone, and coordination.

Choice D: Verbal response is not the first priority, but rather a component of the level of consciousness. The nurse should assess the patient's ability to speak clearly and coherently, as well as their content and appropriateness of speech.

Choice A: Return to hospital immediately if patient is having severe headache or vomiting is correct because it can indicate increased intracranial pressure, bleeding, swelling, or infection in the brain. These are serious complications that can cause permanent damage or death. The patient and family should seek medical atention as soon as possible and not wait for other symptoms to appear.

Choice B: Return to hospital immediately for changes in level of consciousness is correct because it can also indicate worsening brain injury or complications from a head injury. Changes in level of consciousness can include confusion, drowsiness, agitation, or loss of awareness. The patient and family should monitor the patient's mental status and alertness and report any changes to the doctor.

Choice C: Call ambulance if unable to arouse patient is correct because it can mean that the patient has lost consciousness or is in a coma. This is a medical emergency that requires immediate intervention and resuscitation. The patient and family should not atempt to move or transport the patient by themselves but call for professional help.

Choice D: All of the above are correct because they are important instructions for the patient and family to follow when discharging patient home following a head injury. They can help prevent further harm or complications and ensure prompt treatment and recovery. The nurse should educate the patient and family about these instructions and provide them with writen information and contact numbers.