I too experienced the issue with categories. I found the issue was that index.php wasn’t passing the cat query argument into the WP_Query.
This seemed to resolve it:
$cat = get_query_var('cat');
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$the_query = new WP_Query( array( 'post__not_in' => get_option( 'sticky_posts' ), 'cat' => $cat, 'paged' => $paged ));
Aside from that it’s a nice theme.