Retirement tax questions

The 1099-R 2020 with code R belongs on your 2019 tax return but a 1099-R with code R will do nothing to your return.  It seems that you already reported everything correctly in regards to the nondeductible recharacterization ($240) and nondeductible traditional IRA contribution ($350) on your 2019 tax return.  

If you decide to contribute the $6,000 the the traditional IRA for 2020 then follow these steps on your 2020 return (you will enter the previous basis of $590 that was a contribution for 2019, see step 9):

1. Login to your TurboTax Account 
2. Click on "Search" on the top right and type “IRA contributions”
3. Click on “Jump to IRA contributions"
4. Select “traditional IRA”
5. Answer “No” to “Is This a Repayment of a Retirement Distribution?”
6. Enter the amount you contributed
7. Answer “No” to the recharacterized question on the “Did You Change Your Mind?” screen
8. Answer the next questions until you get to “Any Nondeductible Contributions to Your IRA?” and select “Yes” if you had a nondeductible contributions before this tax year.
9. If you had a basis in the Traditional IRA before then enter the amount. (In your case $590)
10. On the “Choose Not to Deduct IRA Contributions” screen choose “Yes, make part of my IRA contribution nondeductible” and enter the amount.

When you decide to convert the amount total amount in the traditional IRA to your Roth IRA in 2021 then on your 2021 tax return you will enter this:

1. Login to your TurboTax Account 
2. Click on "Search" on the top right and type “1099-R”
3. Click on “Jump to 1099-R”
4. Click "Continue" and enter the information from your 1099-R
5. Answer questions until you get to “Tell us if you moved the money through a rollover or conversion” and choose “I converted some or all of it to a Roth IRA”
6. On the "Your 1099-R Entries" screen click "continue"
7. Answer "yes" to "Any nondeductible Contributions to your IRA?" if you had any nondeductible contributions in prior years.
8. Answer the questions about the basis

Only the earnings will be taxable because you had the basis in the traditional IRA.