"Leaving home was a major event in his life." Can I use "incident" instead of "event" in that sentence? Are they synonyms or not?
An event is usually a planned thing. Leaving home, a birth, a wedding, a party, those are generally considered events.
An incident is usually unplanned. It is something that happens unexpectedly, and often there is a negative connotation. For example, at a help desk, people register incidents, meaning that something happened (a bug, a problem, a system failure) that was not only unplanned, but also unwanted.
If you say that leaving home was an incident, you give the impression it happened by accident, and probably because something bad happened.
Events are when something happens that is (most of the time) unusual, whether planned or unplanned.
Incidents, on the other hand, are when something happens and it interrupts something else.
Events and Incidents are not mutually exclusive. All incidents are events but not all events are incidents.
"He got hit by a bus" is both an incident and an event but
"He went downstairs" is only an event but not an incident.
However it also depends on the context of the situation. For example in your case, "Leaving home" is an event on its own, but if "he" is not allowed to leave the house and "he" "leaves home" then it becomes an incident.