How to change commenter links to /user/user_id?

You can use the get_comment_author_link hook, which is part of the get_comment_author_link() template tag, like your question already suggests. Then you only have to get the according user_id, which can be done via the $comment global, and construct the link you want accordingly.

Exemplary usage like shown below:

add_filter( 'get_comment_author_link', 'wpse144835_custom_comment_author_link' );
function wpse144835_custom_comment_author_link( $link ) {
    global $comment;
    $comment_user_id = $comment->user_id;
    // code to create the new link
    return $new_link;
}

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Edit:

Responding regarding your questions, the according comment is unfortunately deleted, so this is kind of a informational shortlist now. There is a lot in there, way too much to really answer them, but I give you some additional information:

• As we have the global available you can use $comment->comment_author

• As for functions, you can use get_comment_author() or comment_author() depending on your need to return or echo.

• At the Codex: Global Variables you can get an overview about them

• There is the WP_Comment_Query and the Walker_Comment class

• For example at the comment_author codex page is a list of comment related functions

• Additionally I’d suggest you look through the comment-template.php and the comment.php to learn more about all of that