If we set up a quarry, power it up and break it in the process of creating frames, the frames will not disappear and we will have to break them manually.

This is unavoidable due to the specifications.
As for the destruction of the frame, the one that touches Quarry is chain-destroyed.

Do you need an item to destroy the frame?

You should not add a new item to destroy the frames, it will be superfluous.