For the rental, you will need to indicate that the rental property was available for rent starting on November 15th instead of breaking it out as being partially for personal use and partially as a rental property.
See this link for more guidance on entering your rental property within TurboTax. This thread also has more detailed information to help you set up the assets for your rental property.
As for mortgage interest and property taxes, yes, you can allocate the amount for the 31 days rented and report those as expenses on your rental activity. The remaining balance would be reported as part of your itemized deductions.
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