Can I do my 2020 taxes on this turbo tax for free today on this computer

Sorry, Online is only for 2021 now. Online for 2020 and prior is closed now so you can not start a new 2020 or prior return or finish one. You have to do each year separately.

How to prepare a prior year return
https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-prepare-a-prior-year-tax-return/00/25984

To do a prior year return you have to buy the Desktop program here,
https://turbotax.intuit.com/personal-taxes/past-years-products
You will need a full Windows or Mac to install it on.

If you want to file for free you can fill out the forms by hand. Here are some basic forms…..

Here is the IRS 2020 Form 1040
https://www.irs.gov/pub/irs-prior/f1040--2020.pdf

or if you want bigger type use 1040SR for Seniors,
https://www.irs.gov/pub/irs-prior/f1040s--2020.pdf

And 2020 Instructions
https://www.irs.gov/pub/irs-prior/i1040gi--2020.pdf

2020 Tax and EIC Tables
https://www.irs.gov/pub/irs-prior/i1040tt--2020.pdf

Sch 1 : https://www.irs.gov/pub/irs-prior/f1040s1--2020.pd
Sch 2 : https://www.irs.gov/pub/irs-prior/f1040s2--2020.pdf
Sch 3 : https://www.irs.gov/pub/irs-prior/f1040s3--2020.pdf

Then when you do file 2021 enter 0 for the 2020 AGI since you are filing 2020 late.

You have to print and mail prior year returns. When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS received the return. Don’t forget state.

Important! Mail Federal and State in separate envelopes and mail each year in separate envelopes.