I would contact the school and ask if there are any services available for your son. Maybe make an appointment with the principal or teacher to advise them of the situation and take your son to the meeting. He needs to see that you are trying to help him resolve whatever is going on in his mind. Writing the letter to the child apologising is also a good idea.

I have heard that children who are bullied then often go on to bully younger children to "reclaim" their power and self-esteem. Doesn't help you I know but this could be a part of why he is behaving this way.

Once everyone has calmed down, have a family meeting with your son, DP and yourself. Talk about the situation calmly and decide on some steps. Make your son part of the solution.

I agree with everything Bathsheba said too.