Yes, you must file 2021 Form 8606 Part I to reported the nondeductible traditional IRA contribution. I would file this with Form 1040-X to explicitly show that there are no changes to income or deductions and to use the explanation space to describe the recharacterization.
Correct, you would say No because you made no distribution that would otherwise be reportable on the 2021 Form 8606.
Correct, Part II of your 2021 Form 8606 will be blank because you did no Roth conversion in 2021. It must appear on your 2022 Form 8606 Part II.
I interpret your last question as indicating that you also made a nondeductible traditional IRA contribution for 2022 and that you also converted that to Roth in 2022. You'll say Yes, you made nondeductible contributions for years prior to 2022 and you'll enter or confirm (if you begin your 2022 tax return by transferring in the amended 2021 tax return file) that TurboTax shows the $6,000 of basis carried into 2022 from 2021. Yes, line 16 will show $12,000; Assuming that you used the same traditional IRA account, you'll receive a single 2022 Form 1099-R for the $12,000 distribution from the traditional IRA and converted to Roth.
