sorry, but the permalink settings have nothing to do with the theme. Unfortunatelly it’s a common problem with WordPress, try searching in Google “wordpress permalinks not working”…
But when you change the permalinks to “Default” and then back again to your custom settings normally than it’s working. You can try also to delete the file .htaccess, then WordPress write a new htaccess file and correct the problem.
a) specific blog posts onto separate page
The problem is that WordPress load posts from the database always ordered by the most recent posts, so if you use a shortcode it will return always the most recent posts.
b) posts from specific category onto separate page
You can link to the categories, see WP admin -> Posts -> Categories.