How do I sell items in the Agency? I can't seem to find it. Is it a feature available only through cash shop, or something? I can buy items from there, but not sell. Server is Rondow if that makes any difference.

what ever you put in your shop will show in auction house you cant put them in auction house itself. =/

How much do shops cost and how long do they last?

u can open shop anywhere in braiken or loa, it cost nothing and last as long as you want
but it keep ur char to stay in town

says i dont have the quest item or some shit when i try to buy from auction house

You need a Veterans Amulet (20% 50% or 100%) equipped to be able to buy from the agency.

"Skillful Battle" amulets will also work.