If a President wanted to pardon "persons unknown who were involved in [a particular activity or event]", would they have the power to do so? Or can a President only pardon named individuals?
Yes, the President could. For example, President Carter granted a mass pardon to those that avoided the Vietnam draft on his first day in office.
Of course, this would have the same limitations that exist generally for Presidential pardons that the President can only pardon a person for federal crimes. If the "activity or event" involved violations of state law, the state(s) would be free to prosecute despite the pardon.