They do have the same reason for spying on Hamlet and Ophelia and discovering the reason for his madness. However, while Polonius wants to find out whether he is right about Hamlet being lovesick, Claudius wants to determine how Hamlet's madness will affect his kingship.
No, I don't think so. Once he start submitting electronic claims, the physician itself may notice that his/her money and time will be spent properly. It may also lessen the amount spent when sending a letter or parcels by mail and may lessen as well the supplies needed. And because electronic claim is actually paperless, in this procedure there is an assurance of financial savings not only for the physician but also for the payers.
A trial is where judged by a panel whereas accusation is when your are acccused, there may either be evidence before or against it.