The witches are sometimes seen as representing fate, or destiny. Do they merely reveal what will happen, or do they manipulate events?

In my opinion, they do not only reveal what will happen, but also manipulate events. When Macbeth approached the witches, they could have concealed the truth from him and just let the events unfold, but they didn't do it. They told him about the prophecy, thus initiating the events that soon followed. If they hadn't told him the truth, Macbeth might have never killed Banquo, Duncan, and the rest in order to become king. So yes, they manipulated events and caused a great tragedy.