Same plane, just stay onboard if the crew is also the same.
Depends on conversion, from 4-8 I believe.
If there is a crew change ask your initial crew and they will know or at least check our station guides for you / if it's all good stay on board if your "booked" / known quantity especially with the new crew who will verify. Also, if customs is required you will get off do the requirements and return depending on the location. Example - coming thru ICN and onward to the U.S. I didn't have to get off at ICN; however, I did get off at ANC for customs and returned to the plane as I was headed to somewhere else in the U.S. because it was an initial entry point for final destination.
Crew size dictates seat opportunity as well as company Dead Headers. One seat remains open for front end crew unless it's only flown by two I believe which does give you an opportunity to shoot for either of the bunks depending on a full house. If three are operating you might still have a cruise bunk depending on other riders. Very comfortable way to get around either way (unless up front like others have mentioned). Unless a pax bird the best thing is No Door...