Is this two separate tickets/PNRs? Otherwise, they should be able to check the luggage through.

Assuming that the luggage cannot be checked through, your sequence seems to be wrong. You would do immigration, baggage claim, customs exit, check in for next flight, and then immigration and security to leave Korea.

KE should arrive at the main terminal, where all of the above would occur. If S7 leaves from the satellite terminal, it's just a bunch of gates (with a few F&B outlets and shops) connected to the area with the other gates by a little underground train. It's really a distant concourse in the airport to which you cannot walk but must take the underground shuttle train.