Deluxe Desktop/CD will handle all these transactions regardless of what you did with the property. If you use the Online edition you would need Premier if you sold the home or converted it to a rental.
Simply inheriting these items does not affect your personal return. The cash will not be reported anywhere.
If you sell the house you inherited then the sale could be subject to capital gains and you would enter it in the Investment section as the sale of a second home.If you turn it into a rental, you would then report the rental income and expenses in the Rental section. Your own personal home deductions, and your second home if you keep the inherited house, will be reported under Deductions and Credits, Your home.
These transactions are reported in the same way in either Desktop or Online, you just need different editions to handle them in each format.
