Sorry for late response... Are you here in korea or still? If not... here's my recommendation You choose ,either a bus or a subway transport.. if you will ride on a bus you'll need to find what number of the bus who will drop you on your hotel place, ($10 for riding a subway ,I think it's same in the bus,there is also a taxi airport but it's so expensive $40 minimum) Upon reaching incheon airport you need to go to the information and ask what bus number are you going to ride(if you'll ride on a bus)but if you will ride on a subway you'll need to ride subway either a ktx (faster than the regular one) or a regular subway,it'll stop in Seoul station then after that you'll need to transfer to another line station it depends on what place is your hotel(pls tell me where's your hotel place so I will tell you the line station are you going to transfer) (You'll need to have a Korean money for emergency,you'll need to buy a transport card in korea that you will use when riding a subway or a bus) upon reaching airport you'll need to ask the information where you can get a ticket that you will use in riding a bus or subway coz you are new.

We subway direct from the airport ( Gimpo ) and it stopped a four minute walk to the hotel. A taxi would be expensive, 50 USD ++ is best guess. Yes, lift in lobby. Very convenient for the markets you mentioned. All w/in 15 min walk, or a couple subway stops.

it is actually located on the center of insadong art street.... you can go to insadong information center which is located outside of that art street and they will give you a map..