For the layover hotel, you have to call KE first and arrange it by filling out a form. Then when you arrive at ICN there is a special Korean Air Stopover Hotels desk (they will tell you location).
The cheapest fares like N, T and mileage awards don't get it.
You can also request a hotel in the city of the Seoul (about 1 hr from the airport to main downtown area) if you want to go in for some sights. Otherwise, the default hotel is the Grand Hyatt right next door to the hotel (as it's owned by KE).
Personally, I always book on the airline's website directly to avoid any hassles with IRROPS etc.