View rest/page copycat In view, when I set the settings to field field1 in Page, the same settings apply to field1 in Rest export. How do I get rid of it? 

I see that everything is copied. I deleted the field from Rest export, and it disappears also in Page.
When you click on add / remove / edit a field / filter / sort / contextual filter etc.. at the very top, you need to change the For All displays to This page (override) so it does not affect all the other views. You only need to do this for the first time, it will remember your setting. 

Note: field / filter / sort / contextual filter etc... each have individual settings.