I’m not sure what you mean when you say
it’s the Genesis Framework, so there is no custom menu setup
Genesis does support Custom Menus if you go to Appearance > Menus in the admin area, you should be able to control the menus from there.
Or, maybe you meant to say “it’s not the Genesis Framework”?
Are you using a version of WP that allows you to use Custom Menus?
I would think that you just need to go to the the Menus in the back end and Add the desired Category to the Menu that is being used for pages.
Regarding the second question:
There’s a function you can add to your functions.php file that will remove the Post Meta that you’re describing.
You can find that code snippet here: http://my.studiopress.com/snippets/post-meta/#remove
In your style.css for Generate, find -
and add -
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