Recharacterization and conversion in different amounts and different years for same tax year

In 12/20 - I contributed $3K to a new Roth IRA for tax year 2020

In 3/21- after filing tax return, realized I exceeded income limits

In 3/21 - recharacterized this $3K from Roth to tIRA (received Form 1099R - Code R)

In 3/21 - contributed additional $4K to this same tIRA (to max out $7K contribution - over 50)

In 5/21 - did back door Roth conversion of $7K from tIRA to Roth IRA (received Form 1099R - Code 2)

In 5/21 - filled out Form 8606 manually to reflect total basis in traditional IRA's for 2020 of $7K, Part I only

In 2/22 - contributed $7K to tIRA for tax year 2021

In 2/22 - did back door Roth conversion of $7K from tIRA to Roth IRA for tax year 2021

Question: Do I owe 6% penalty on the $3K for over-contribution in 2020 even if I recharacterized in 2021?

Question: Do I still need to amend 2020 tax return for the recharacterization if I already submitted Form 8606 manually? If I need to amend, I'm not sure how to answer the questions in Turbo Tax to reflect a recharacterization of $3K but a total basis in traditional IRA's of $7K.

Question: for tax year 2021, should I report the $7K  contribution made in 2/22 on Form 8606 for 2021 to reflect a basis of $14K ($7K for 2020 + $7K for 2021), and then record the conversion in 2022?

I reviewed other postings to find similar situation, but could not find anything.  Any assistance would be greatly appreciated!