Is it unreasonable for me to request blood work for my 4 yr son who has had only a fever of 104 for three full days? Doc says no need, just a virus.

Not unreasonable. It depends on the big picture, and the doctor-patient relationship. It is not unreasonable to ask for a blood test. The doctor may agree or disagree on testing, because it depends on the symptoms, past history, etc... At my office, we check for strep throat and the flu, as this is flu season. If the exam is negative, and the child is happy, we worry less. If the child looks sick, we do more tests.
Hard to say. The best judge of whether or not to order tests is a well trained primary doc who has reviewed the history and done the exam. Many ER docs automatically order blood tests on every patient( to keep the complaint letters at a minimum) and it is common for adult clinics where chronic conditions are monitored this way. You either need to trust your doc's judgement or find one you can.
Judgement call. depends on history, physical exam, and clinical impression, if those warrant any further studies the doctor who made the decision would proceed with such. if that was the only symptom and no signs of serious illness, then no need for further workup, trust your doctor, although a second opiniuon is your right, wish yourself and your son wellness.