Rented out principal residence and in the same tax year 2020, bought another home which I currently occupy as principal residence

Hello Tax Experts,

I really need help for my scenario below:

I was living in a Condo Unit in CA from Jan-August end in 2020. From September 1st 2020 I rented out this condo. I bought another home in CA in July 2020, the previous owner did a rent-back and he stayed in this new home for 28 more days after I purchased it. I moved into the new CA home in August end.

Hope I was clear on my scenario. Now my questions are:

1. Which home do I list as my Principal Residence in 2020, the condo or new home?

2. Do I need to show 28 days rental for new Home as rental Income, although this Rent was pretty less and not the actual fair market value rent?

3. For property taxes, mortgage principal and Interest deductions, Depreciation etc. how do I fill this in Turbotax Desktop for Mac

I am really confused at this point and would highly appreciate your inputs on this.