I apologize. I thought I answered the first two questions in a general answer, however I did neglect to answer your question on estimated taxes on Form 593E. This is answered at the bottom, last.
You NEVER include the same $s of RE tax paid, in two places. RE TAX IS DEDUCTIBLE on SCH A FOR THE TIME PERIOD YOU OWNED THE PROPERTY. Any other real estate taxes allocated on closing statement may have been for DELINQUENT TAXES and are ADDED TO BASIS of the property.
General Rule:
Deduct on schedule A: RE taxes for the period you owned the house.
Closing Statement when you bought the house: Only taxes included that will cover your period of ownership (2-28-17 forward) prorated to you (presumably because seller already paid)-deduct on schedule A only.
2nd closing when you sold: If you paid(or had previously paid) real estate tax owed by the buyer (beginning on the date of sale), the buyer is considered to have paid the tax. THE SELLER TREATS AS REDUCED SELLING PRICE.
Special assessment-time period before 6-30-17- you owned, therefore deductible schedule A.
I do not understand after 7/1/17 -7/7/17- If you were the owner then goes on schedule A
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