Yes, the work specifically for the solar (such as stronger structural support) is added to the Cost Basis.
The credit that you received reduces the Basis.
The Basis for depreciation is the lower of (1) your Adjusted Basis (see prior two sentences) or (2) the Fair Market Value when it was started to be used for business/rental. Then the business/rental percentage is applied to that number.
The 5 year recovery period for depreciation starts when it was "placed in service" for rental. So the 5 years starts in the fall of 2018 for you.
