custom post type – project link output via single-portfolio.php

You can always use WordPress Code Reference to understand what is going on:

get_post_custom() is a function that retrieves post meta fields and needs a post id as an parameter. It returns an array with post meta for the given post:
https://developer.wordpress.org/reference/functions/get_post_custom/

get_post_custom_values() is a function that retrieves values for a custom post field and accepts the key and the post id as parameters. It returns an array of meta field values.
https://developer.wordpress.org/reference/functions/get_post_custom_values/

So you need the indexes to access the first position in the arrays. If you want to take a look at the the indexes of the array, you can output them like:

$key_values = get_post_custom_values( 'project-link' );

echo $key_values[0];

This will show you what the array contains on index position 0. Try it with 1 or 2, if you want to see whats inside of these index positions.

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The other question was, how you get the desired output. First of all you want to show the url, so you have to put it between the a tags:

<a href="https://wordpress.stackexchange.com/questions/366797/<?php echo $link[0]; ?>" target="_blank"><?php echo $link[0]; ?></a>

And if you want to put it below your content, you need to put your the_content() call above the a tag. Also I guess you should use it inside your post loop and use the function get_post_custom_values with the post id:

<main class="view">
    <?php
        while ( have_posts() ) :the_post();
            the_content();
            $current_post = get_the_ID();
            $link= get_post_custom_values('project-link', $current_post); 
            if($link[0] != "") { ?>
                <a href="https://wordpress.stackexchange.com/questions/366797/<?php echo $link[0]; ?>" target="_blank"><?php echo $link[0]; ?></a>
            <?php } else { ?>
                <em>live link unavailable</em>
            <?php }
        endwhile;
    ?>
</main><!-- .site-main -->

Hope this helps and I understood your question correctly.