Yes, you will have to enter your 2020 W-2 on your 2020 tax return because right now TurboTax believes you had no earned income and therefore you would not be allowed to make the contribution.
No, you should have a $6,000 basis on your 2020 Form 8606 line 14 (assuming you had no prior basis left in the traditional IRA from 2019 and earlier). You made the $3,000 contribution to the traditional IRA and you recharacterized another $3,000 to the traditional IRA and made these nondeductible therefore you will have a total of $6,000 on line 14 to carry over to 2021.
It seems you have entered the traditional IRA and recharacterization correctly.
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