Yes, when you copy a page you're creating a new page with the same content as the page you're copying. So the Creation Date and Original Creator will be as if you're just creating a new page.
One lesser-known fact as well: People who were watching the original page won't be watching the copy, so if you want the same people to watch the copy, you either need to tell them to watch it, or, if you're a space administrator, you can click Manage Watchers on the Watch panel and add watchers to your new page. Hope that helps.
If you move a page from one space to another, it won't affect the Creation Date or Original Creator. These are properties of the page that moved with the page, as is the complete history of the page.
I've just tested this by moving a page created by another user from one space to another, and then back again. The Creation Date and Original Creator have not changed at all. Do they change when you move a page to another space?
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