Amended previous year return, do I need to re-import and start 2021 again?

No, when you imported the federal, the state should have been imported along with it. 

So what happens to changes I made to 2020 State file (amended return). These changes I did after the import. How do I carry those changes over or I can safely ignore?

It depends on the change you made, but honestly I do not know of very many carryovers that would only apply to the state and not the federal tax return. Meaning if you only needed to change the state and not the federal return, there would be no carryovers coming with that change.  Therefore it would have no affect on the current state tax return.

However, if you plan on getting money back from the state with the amend, it will affect the state and local tax deduction on the federal side this year. If you are taking the standard deduction this year, then you are fine.