When applying liquify for a high res image, the resolution of the liquify window is very low. Preview is difficult and blurry.
This guide shows you how to zoom in effectively and apply liquify on selected region.
Zoom In for Photoshop Liquify
Yes, that works well.
I like to cut/paste so that I can have a few versions/layers to choose from.
I don't see an advantage to copying and pasting in a new document. I select the area I'm gonig to work on, copy it to a new layer, and apply liquify to that.
Why move the selected piece out of the document and then back in?