inserting a category into post

I haven’t tested the code below, but I think you could use something like it.

add_shortcode( 'show_posts_from_cat', 'wpse_85708_posts_from_cat' );

function wpse_85708_posts_from_cat( $atts ) {
    extract(shortcode_atts(array(
        'id' => ''
    ), $atts));

    $args = array( 'category' => $id );
    $cat_posts = get_posts( $args );

    foreach( $cat_posts as $cat_post ) {
        setup_postdata( $cat_post );

        // Display code here.
        return apply_filters( 'the_excerpt', get_the_excerpt() );
    }
}

In this case [show_posts_from_cat id="1"] will show all excerpts from the posts of category with id 1.