Rerouting is a change in the cities involved in the ticket. I don't know if it includes changes on the connections (for example, switching from STL-CVG-CHA to STL-ATL-CHA).

Transfers are another word for connections--they happen when it takes more than one flight to get from point A to point B.

Combinations are putting two separately priced flights on the same ticket. For example, if the fare from ATL-YYZ plus the fare from YYZ-YEG is lower than the single fare ATL-YEG, you can put the two flights on the same ticket. (That is a simple variety, known as an end-on-end--there are others.)

Co-terminals are airports that count as the same for purposes of defining roundtrips. For example, if you fly LAX-EWR in one direction and LGA-SNA in the other, that's still a round trip--the three NYC airports are co-terminals, as are the five in the Los Angeles area. (Other common examples in the States are the three in the Baltimore-Washington area, the three in South Florida, and the two in Houston.)

Can't help you on the open-jaw question.