If you have not started advertising as available to rent and/or actually renting the property in 2020, then you would not include the rental property on your 2020 tax return. If you have only been renovating it up to this point and then you will release it to be rented (May 2021), then it will be 'placed in service' in 2021 and will be reported on your 2021 tax return.
At the point that the property is placed in service, the improvement costs incurred prior to the placed in service date are added to the cost basis for depreciation. It doesn't matter which year the money was spent if it was prior to the placed in service date.
Yes, the software will help you enter all associated amounts needed to calculated the cost basis for depreciation for the rental property. This will include the purchase date, date placed in service, original cost, improvements, and other items.
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