Regarding the number of pages displayed, read through the arguments for paginate_links, specifically end_size and mid_size.
As for the 404- The problem is there is no page 3. Whether or not a page returns content or loads the 404 template is based on the results of the main query, not your custom query you run in the template. If this is a page post type, try setting the paged query var instead of page.
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