get comments by current user inside page template

This is not working and also I don’t know how can I get the comments
of the current user.

You have already used the current user’s ID in your code…

echo 'User ID: ' . $current_user->ID;

… but you hard-code a single ID in the get_comments argument array. Don’t do that. Use the current user ID.

$args = array(
    'user_id' => $current_user->ID, // use user_id
    'post_type' => 'my-CPT',
);

I am uncertain of the relationship between your user comments and wp_list_comments. You have already output the user comments so I don’t why you are running wp_list_comments unless you are trying to output a different set of comment or you are trying to output the same comments again (which is weird). Either way, you need to pass wp_list_comments a set of comments as in this example from the Codex (re-formatted to be less confusing):

//Gather comments for a specific page/post 
$comments = get_comments(
  array(
    'post_id' => XXX,
    'status' => 'approve' //Change this to the type of comments to be displayed
  )
);

//Display the list of comments
wp_list_comments(
  array(
    'per_page' => 10, //Allow comment pagination
    'reverse_top_level' => false //Show the latest comments at the top of the list
  ), 
  $comments
);

Note the second argument $comments, which is the output of a call to get_comments. The context you seem to be using this in makes me think that that is going to be required.

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