is it possible to set the "add page" permission (permission to add pages in confluence) and the "edit page" permission (permission to edit existing pages in confluence) separately?
No. They are the same permission because it doesn't make a lot of sense to allow someone the right to do one and not the other. Especially on a wiki, where people draft stuff and are positively encouraged to edit later.
What's the aim though? There may be a good way to achieve what you want without thinking about permissions.
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