Are events triggered when the NON-current player's token moves over them?
The rulebook does say that only when the current player marker moves over an event icon during the advance initiative marker step are the events resolved. If the non-current play has their token moved over an event space by a combat card, the event should not be fired?
The event should not be fired.
If the current player's token moves over an event space due to combat card play, rather than advancing the marker after orders, does the event happen?
Possibly. Depends on whether or not his marker is past the opponent's marker, and is this the first time that event space has been passed/landed on.
The sequence of play description on page 14 possibly could have been written a bit clearer. The check for change in Initiative happens during Step 3. At this point, if the current player's marker has been moved beyond the other player's marker, the Coexistence battles and Special Phases kick in. It doesn't really matter how the marker got moved. If current player's marker has passed the other, these special actions occur.