When a 17 year old is charged with assault are the fines and court costs at the expense of the parents?

Based on the facts you presented, it is my recommendation that you meet with and retain an attorney familiar with the local court. This is particularly important given the fact that there is video and a statement from your child. Many attorneys offer free consultations and will be able to offer detailed information the pending matter. A defendant is responsible to pay fines and costs associated with a criminal conviction. In fact, I have had experiences where a Judge is frustrated when parents pay for a child's mistake. Having said that, this is is a question better left to local counsel. You should hire an attorney.