1) You can leave Form 1099-R with code R it won't make any changes to your return.
2) Yes, you will enter $6,501.34 as converted (the amount you moved from the traditional IRA to the Roth IRA).
3) Yes, your 2022 Form 8606 looks correct. You have a $6,000 basis to carry over to 2023 and $501 of the conversion (earnings) is taxable.
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