Delicacy.
Is cheese.
And Yes you can keep using the same Item to re-enter the Fairy Area.
Grind for plenty of credits before doing this. Go to the New Ark City slums, in the area with lots of homeless people in it, one guy asks for food. Rest and keep giving him food until he tells you the junk merchant in the market also sells counterfeit Upper New Ark passes. These cost 100 credits, however don't try using them and instead visit Happy Massage right after. After a session, Lin Lin shows you to TAT2 where you can now get a counterfeit pass which works 100% of the time for 500 credits each. Go to the mall in Upper New Ark then up the escalator to obtain the refinery, heater, and an additional fridge.
Also, junk is free to take.
Probably a little too late for this to be relevant, but one thing to note is that if you have a Quality Counterfeit Pass in your inventory, you can craft another one using an Ink Pen (from the Hardware store) + bad pass, though it requires passing a Nimble check (I believe you need 12 for it to be about 50% odds).