You can just enter the property tax paid on your house with the other property tax- you do not have to report the address of the home to the IRS, but keep the records with your tax documents (that show when you sold the house and the tax charged)
To be clear, just add the property tax paid and enter that into schedule 2 line 2?
You can enter on Property (Real Estate) Taxes under Deductions & Credits. You can enter it as Property Tax on Your Main Home because it was your main home for part of that year.
This is where I add the property taxes for both properties, right?
There are two places in the program/interview where you can enter property tax. You can enter taxes for both properties under Deductions & Credits >> Property Taxes. If you do enter both here, do not enter again when entering your Form 1098 for mortgage interest.