There’s not a way to keep an entire category private. At least not one I can think of off the top of my head. There is the exclude_category shortcode option but that does not really make the entries within private.
I’m assuming you’re using a template which supports pagination, yes? Pagination can be disabled using the
enable_pagination shortcode option. You would add it to the shortcode, setting it to
false like so:
One recommendation … I really do not recommend showing much more than a max of 50 as that could negatively impact page load times. Pretty much for the same reasons as why WP limits posts to 5 or 10 a page.
I hope this helps!