Related posts and home page number of word limit

The theme does not use the related posts shortcode. You may want to try a plugin such as this one for this particular functionality:
http://wordpress.org/plugins/contextual-related-posts/

To display the_excerpt instead of the content, copy loop.php from your parent theme into your child theme and edit line#137 (the_content) to:
<?php the_excerpt(); ?>

To change the number of characters displayed, see here:
http://codex.wordpress.org/Function_Reference/the_excerpt

Specifically in your child theme functions.php, use:

function custom_excerpt_length( $length ) {
	return 20;
}
add_filter( 'excerpt_length', 'custom_excerpt_length', 999 );