Two Roth 20/21 recharacterizations, plus one backdoor conversion

No, if you entered the recharacterization on your 2020 return like mentioned below then you do not need to amend your 2020 tax return. A 1099-R with code R will do nothing to your return. You can only report it as mentioned below. Therefore, you can ignore the 1099-R with code R.

You will enter the recharacterization when you enter the contribution to the Roth IRA

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 “Roth IRA”
5. Answer “No” to “Is This a Repayment of a Retirement Distribution
6. Enter the Roth contribution amount 
7. Answer “Yes” to the recharacterized question on the “Did You Change Your Mind?” screen and enter the contribution amount (no earnings or losses)
8. TurboTax will ask for an explanation statement where it should be stated that the original $xxx.xx plus $xxx.xx earnings (or loss) were recharacterized.
9. On the screen "Choose Not to Deduct IRA Contributions" answer "Yes" (if you are thinking about doing a backdoor Roth. If you have a retirement plan at work and are over the income limit it will be nondeductible automatically and you only get a warning and then a screen saying $0 is deductible)

When you make the contribution nondeductible TurboTax will create Form 8606 and you will have a basis on line 14 to carry to 2021 (enter for your spouse on the 2021 return when entering the 1099-R for the conversion with steps 11 and 12).

For the 2021 return, you will enter recharacterization with the steps above.

You will enter Form 1099-R with codes N but they won't be taxable. For the conversion you will enter the 1099-R like this:

1. Click "Federal Taxes" on the top and select "Wages & Income"
2. Click "I'll choose what to work on"
3. Scroll down and click "Start" next to "IRA, 401(k), Pension Plan (1099-R)" 
4. Answer "Yes" to the question "Did You Have Any of These Types of Income?"
5. Click "I'll Type it Myself"
6. Choose "Form 1099-R, Withdrawal of Money from 401(k) Retirement Plans, Pensions, IRAs, etc."
7. Click "Continue" and enter the information from your 1099-R
8. Answer questions until you get to “What Did You Do With The Money” and choose “I moved it to another retirement account”
9. Then choose “I did a combination of rolling over, converting, or cashing out money.” and enter the amount next to "Amount converted to a Roth IRA account"
10. On the "Your 1099-R Entries" screen click "continue" after you entered all Form 1099-Rs
11. Answer "yes" to "Any nondeductible Contribution to your IRA?"
12. Answer the questions about the basis from line 14 of your 2020 Form 8606 and the value of all traditional, SEP, and SIMPLE IRAs

No, you do not need to pay the 6% excess contribution tax since you recharacterized your contribution before the due date (assuming you had enough taxable compensation like wages to make the contributions).