Detailed step by step information here: http://asiaenglish.visitkorea.or.kr/...K_EN_2_2_4.jsp

You cannot use the all stop train. You have to use the express. Don't worry, it's only 4,000W more for the express, so not too expensive.

Yes, you can walk around pre-security. Honestly, with two hours, there's not much to do except eat at a restaurant. There's more shopping and stuff (like cultural experiences) to see/do inside.

The website says "proceed directly to the special security area," which just means "you don't have to go to an airline counter. The special security area is also the flight crew/diplomat line.

Even more important.... you can use check in at Seoul Station ONLY if you are flying Korean Air, Jeju Air or Asiana. AND you must check in three hours before your flight at the latest.

If you're staying in Gangnam, I'd suggest City Air Terminal if you want to try the system. They also accept MANY more airlines. Like essentially every one.