Is there a free market in property inside the walls of Westeros’ major cities and how would such a system be incorporated into the wider medieval/feudal environment outside the walls

Buildings on land could be bought and sold more easily than the land under them, but any expert on English land law will tell you that the intricacies of medieval leases doesn’t quite resemble a free market. (For one thing, given that the mortgage didn’t exist, you certainly couldn’t get secondary markets.)