There are fuel surcharges in principle, but some airlines do not collect them for other airlines. So if you issue on AA ticket stock and have no AA intercontinental flights (so no AA surcharges) then you will get no surcharges. If you issue exactly the same itinerary on CX or BA stock you will get a lot of surcharges because they collect their own and other carriers' surcharges.

In principle any OW carrier can issue any itinerary. In practice it can be hard to convince them if none of the long segments are on their flights. But certainly the ticket doesn't have to be issued by the carrier of the first flight.

Even as a CX Gold I have had CX ticketing deadlines of 7 days - possibly because it was HKG-JFK in A (a high demand route).