Answer to Question 1
A good that is offered at a price of zero may not necessarily have been produced at zero opportunity cost. Often stores give away free products to get customers to try them but these products were probably not produced at zero opportunity costs. By that definition they are not free goods.
Answer to Question 2
Rent seeking is the act of obtaining special treatment by the government to create economic profit or to divert consumer surplus or producer surplus away from someone else. Often, rent seeking takes the form of lobbying to increase the economic profit of the lobbyist. Rent seeking increases the deadweight loss from monopoly. With rent seeking, not only does the monopoly create the (standard) deadweight loss, but also resources are used up in the process of rent seeking itself.
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