Make custom page look exactly as homepage

Need more info please.

You can copy and rename the file something like page-template.php and add a page template header.

//* Template Name: Your Page Template Name

or

You could rename the file home.php and pre_get_posts to control which category of posts it displays:

function my_home_category( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', '123' );
    }
}
add_action( 'pre_get_posts', 'my_home_category' );

It depends on how the loop is generated in your theme.