I figured out the template issue for individual custom posts. Here is the answer in case anyone else needs it:
Say you have a Custom Post Type called “Events.”
You need to create a new template file called single-events.php
(I just duplicated single.php and changed its title and fiddled with the inside a bit to remove stuff I didn’t want showing up for this custom type.)
And if you want to add individual custom fields to the inside of the template, here’s the PHP code:
<?php echo get_post_meta($post->ID, 'field-name',true) ?>
You would replace ‘field-name’ with the name of your field — in the case of the Events post type, for example, that would be ‘location’, like this:
<?php echo get_post_meta($post->ID, 'location',true) ?>
— Maria