I'll try to be succinct.
Gareth will sell you the shed, play nice, improve your friendship with him and bring up in conversation that he should already know that you paid for the shed and are waiting for him to give you the key. Keep prompting the Ai to figure out that it owes you the shed key and it should, eventually follow through. Other than that interaction I recommend avoiding conversational trades until you have saved right before it and have the patience to fight through a lot of attempts. Sometimes it's expert and flawless, sometimes I give up and will try again later..
Your property is an invisible box between the river, the tavern and Rosalyn's home. Three eyes showed one screen shot once that gave a map of it, or a portion of one, Basically, you can build on your square when you have the key, and one other residents' squares when they give you a key to their place.