Property taxes can be itemized on the schedule A itemized deduction of the 1040, or if your standard deduction would be more than your itemized deduction, the amount can be used to increase your standard deduction amount on your federal income tax return.

Itemized deductions must exceed the standard deduction amount set by the IRS for your filing status. Common itemized deductions include mortgage interest, state and local taxes, and charitable donations. Additionally, your total itemized deductions should result in a greater reduction of taxable income compared to using the standard deduction.

Yes

Makes it go down.

Some of the refund amount could be taxable if you itemized deduction in the year and claimed the estimated tax payments as a part of your itemized deduction for that year.