Yes, it's possible to sell a house in Arizona without a Realtor. “For sale by owner” listings are fairly common, but if you're considering one, make sure you're prepared for how much work you'll have to put in.
Property taxes are due and payable in two installments: The Seller is responsible for all taxes due or delinquent up until the closing date. The Buyer is responsible for all taxes due after the closing date. A proration is a proportionate share of an expense, charged to the party responsible at time of closing.