There is no way to clear immigration AFTER a transfer. There is no arrival lounge like you are looking for. You need to follow signs for Arrivals and clear immigration first to enter Korea. In the basement of T1 is Spa on Air, a Korean sauna. That is the only thing available right on arrival.
If you follow transfer signs, you will stay airside. You cannot simply leave airside. So, I would enjoy Seoul and then arrive back to the airport early to enjoy the lounges and showers if you don't want to use the sauna.
AC is in T1 as is OZ. If the lounge showers are full, check out the Rest & Relax area on the 4th floor airiside. Free showers for transit passengers and all things are included. They're just as nice as lounge showers.
Matina food is ok by Western standards. It's normal fried rice, Korean/Chinese dishes, fruit, etc etc. Bibimpbap station. It is no Cathay Pacfic. Koreans LOVE it because well, it's typical Korean quality buffet. Meaning - give them ramen and some fried saucy foods and they are happy!