That is correct, if you have a ticket from ICN to PUS, then immigration is handled at the end, PUS. This was changed within the last few years and now ICN/PUS flights are considered international flights in Korea. The ICN/PUS ticket usually can only be purchased with proof of a flight arriving or leaving ICN. Saves the hassle of going through immigration at ICN, and then getting on a bus to GMP airport to take a domestic flight to PUS.

As for the first class ticket on KTX, I would recommend purchasing the normal economy fare. Then go back to the ticket counter to upgrade it to First class. Pay the difference out of pocket. You may be able to purchase the Tickets Online online before. It is maybe USD $20~25? In First class, the seat layout is 1-2 arrangement. 'A' seats are solo, while 'B' and 'C' seats are together. If you have a choice, the A seats are preferred as it is both Aisle and Window. Btw, it is First Class in name only! Seats are roughly comparable to domestic airline biz seats. But still worth the upgrade as economy is cramped and I would not want to be stuck there for 3 hours.