The answer depends on when and how the distribution from the Roth IRA was made. When was this distribution made? What is the code in box 7 of the Form 1099-R reporting the distribution from the Roth IRA? If the corrective distribution was after April 15, 2021, it could only be done by a regular distribution and 2020 Form 5329 Part IV would need to be filed stand-alone and the 6% penalty paid with that.
No.
Second questions:
The corrective distribution should have been done by a return of contribution. Assuming that this was done in 2022, this will be reported on a 2022 Form 1099-R with codes J and P in box 7, the sum of $3,400 and the earnings in box 1 and just the earnings in box 2a. You can enter this now in 2021 TurboTax as if you've already received this form and TurboTax will include the earnings on Form 1040 line 4b and on Form 5329 line 1. (If the corrective distribution for the $1,250 excess contribution for 2020 was made after April 15, 2021, Form 5329 will also show this distribution on line 20 to eliminate the excess carried into 2021 which should be present on line 18.)
As far as I know, no state assesses an excess contribution penalty, but as least one state (California, 2.5%) assesses an early-distribution penalty which would be due on the earnings distributed.
