The correct answers to these open questions are the following.
What are the advantages and disadvantages of the use of presentence investigation reports?
The advantage is that this kind of background investigation can lead to a considerable reduction of the sentence if the authority finds a considerable reason to do so. On the other hand, the disadvantage or risk is that a failure in the investigation provokes an incorrect decision about the right sentence for the criminal.
Should factors such as education, family, work history, and prior criminal history have an impact on sentencing?
Yes, they should. That is part of the investigation. If the criminal has had a previous "normal" life, with no serious conflicts at all, those factors can be contemplated to reduce the sentence of the individual.
Should any external factors make a difference? Yes, that is why there is this kind of investigation. The probation officer has the responsibility of preparing this presentence investigation report and has the faculty to consider the element it deems necessary to severely punish a criminal or reduce the sentence to help it.