1) No, as long as you don't have pre-tax funds in the account on December 31, 2023, the pro-rata rule will not apply.
2) You will enter your 2023 Form 1099-Rs for the rollover and the conversion in the retirement section and enter the basis from line 14 of your 2022 Form 8606 when TurboTax asks "Any nondeductible Contributions to your IRA?". Please see How do I enter a backdoor Roth IRA conversion? for detailed instructions.
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