I qualified for the free file edition in 2020. I want to amend it. Can I purchase the 2020 Deluxe version and import the Turbo Tax free file from that year to amend it?

If you need to file an amended return for a prior year you need to use the same version you used to file the original return.

Yes you can open the .tax2020 file in any Desktop program.  You can buy Deluxe for 2020 here, 
https://turbotax.intuit.com/personal-taxes/past-years-products/2020/ 

After you get the program installed the first thing to do before you open your tax return .tax file is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW).  Just enter some basic personal info like your name and address then click on the State tab at the top and it should ask if you want to download the state program.