Flights between regions don't count against the segment count in either region but of course count against the 20-total limit. A stopover at a gateway city counts against that region's stopover total, if there is one.

While you're absorbing rules, don't miss the one that says you can't fly through your origination city (at least for OWE - I've never done GE). That's pretty easy to adhere to if you originate CAI but for instance if you originated LON and came back there thinking you'd use a couple of European segments, you couldn't.