The UA flight (mentioned fairly often) is a tag on the LAX/SFO-SYD service, as you surmised. There are no traffic rights granted on the segment in exclusivity, but it IS OK for the RTW (though you sometimes have to correct an agent on this).

Rerouting *should* be easier, I would think, but if they get confused they don't have any paper to stare at. I'd think the potential for something to get screwed up might be higher. I'd certainly always ask for a new printout/email of the itinerary and check it before walking away/hanging up. Changing dates would be a snap, just as it was with the paper ticket.

On United, supposedly status no longer has to be re-entered as they have upgraded their computer system. And it's usually the airline that does it. You can always just have it confirmed when you check in for a flight (or print out the new online record as well).