ROTH contributions for 2020 would be reported on the 2020 return but you would only need to amend the 2020 return if you are eligible for the Saver's Credit form 8880 otherwise there is no need to amend the 2020 return. Only the 2021 contributions are mentioned on a 2021 return.
No, you do not add both to your 2021 return.
Yes, you would need to amend your 2020 taxes to add the contribution for 2020 to your 2020 return. But the deadline to make contributions for 2020 was May 17th and you stated you made the contributions in June 2021. Are you sure about that date? If yes, did your financial institute really apply it for 2020 (they should not have done that)? You might have an excess contribution.
To enter your contribution for 2021 on your 2021 return: