Inserting an example of the last 3 post on to the homepage

Question

From what I can understand, you are talking about a static front page as you are referring to a template called homepage.php. The standard homepage uses index.php.

To achieve 3 latest posts, you will need to create a custom query using WP_Query. I’m not sure which parameters you need, but feel free to read throught the given link and just add them as needed to the arguments. It also seems from comments that you have trouble swithing between php and html. You will need to check out examples in tutorials for a proper explanation. I will in my code add a basic div class to the title and excerpt. You can expand and explore this further

This is a very basic example of what you need: (Just remember, this query defaults to query the post post type. If you are using custom post types, you need to set the post_type parameter)

$args = array(
    'posts_per_page' => 3,
);
$q = new WP_Query( $args );

if ( $q->have_posts() ) {
    while ( $q->have_posts() ) {
    $q->the_post();
        ?>
        <div class="title">
            <?php the_title(); ?>
        </div>

        <div class="excerpt">
            <?php the_excerpt(); ?>
        </div>
        <?php
    }
    wp_reset_postdata();
}

EDIT

From your update, the following notes:

Never ever use query_posts. It breaks page functionalities and the main query
show_posts should be showposts and is btw depreciated. You should be using posts_per_page