I have an Apex application (v 4.2) which uses a page zero, and one level navigation tabs. Is there any way to create a new page which still uses the navigation tabs, but doesn't inherit page zero?
What exactly are you trying to do? What do you mean by "one level navigation tabs"? Standard tabs are rendered by the page template, not by a region.
To suppress a page zero ("global page" in new terminology) region, use a Current Language is not contained within Expression 1 condition on the global page region, and create a region with a different definition in that display position on the new page.
Or can I create a 'different' page zero and have some pages inherit that instead?
No, APEX currently only permits one global page for each user interface type defined for the application.