this is wordpress defult table, 

$wpdb->update($wpdb->commentmeta, ...) -- this is working

but this one is not a defult 

$wpdb->insert($wpdb->wc_users_voted, ...) --- this is not

This $wpdb->insert($wpdb->wc_users_voted, ...) should be a $wpdb->insert('wp_wc_users_voted', ...)

But when I used commentmeta, I didn't put that prefix and it worked.

$wpdb->update($wpdb->commentmeta, ...) -- this is working

$wpdb->insert($wpdb->wc_users_voted, ...) --- this is not

There is no such a $wpdb->wc_users_voted table in the wpdb. You should replace this {$wpdb->wc_users_voted} with this wp_wc_users_voted string. 

In your case, the wp_ can be different. 

I didn't set show_errors() before...

if (wpDiscuz()->options->thread_display ) {
                do_action("wpdiscuz_reset_comments_cache", $postId);
            } else {
                do_action("wpdiscuz_reset_comments_extra_cache", $postId);
            }
            do_action("wpdiscuz_clean_post_cache", $postId, "comment_voted");

do the job.

The insert statement on wc_users_voted table doesn't add new row (and $wpdb->last_error is just empty string). Maybe I'm making a mistake somewhere:

$vote = 1;
$date = current_time("timestamp");
$userIp = md5(getUserIP());

// $commentId and $postId are valid numbers and getUserIp() return my ip address

$sql = $wpdb->prepare("INSERT INTO `{$wpdb->wc_users_voted}` (`user_id`, `comment_id`, `vote_type`,`is_guest`,`post_id`,`date`)VALUES(%s,%d,%d,%d,%d,%d);", $userIp, $commentId, $vote, 1, $postId, $date);
$wpdb->query($sql);

Please use this one: 

if (wpDiscuz()->options->thread_display ) {
                do_action("wpdiscuz_reset_comments_cache", $commentId);
            } else {
                do_action("wpdiscuz_reset_comments_extra_cache", $commentId);
            }
            do_action("wpdiscuz_clean_post_cache", $commentId, "comment_voted");

I see that options is a WpdiscuzOption object with dbManager as parameter (WPDiscuzCore.php)

$this->dbManager = new WpdiscuzDBManager();
$this->options = new WpdiscuzOptions($this->dbManager);

Can I get the meta_value field from comment_meta in my endpoint, change it and then update the comment_meta database?

Yes, you're right. 

Also with the wc_users_voted table but I see that I will need to add new row there (although there is an UPDATE statement in updateVoteType). The user_id will then need to be an ip address of the user if I'm right?

This is also correct. You can use the user IP as a value of the user ID. Just a bit of correction. You should use the INSERT instead of the UPDATE statement in updateVoteType. 

Also, please use the code below for deleting the caches:

if ($this->options->thread_display) {
                do_action("wpdiscuz_reset_comments_cache", $commentId);
            } else {
                do_action("wpdiscuz_reset_comments_extra_cache", $commentId);
            }
            do_action("wpdiscuz_clean_post_cache", $commentId, "comment_voted");

Can I get the meta_value field from comment_meta in my endpoint, change it and then update the comment_meta database?

Also with the wc_users_voted table but I see that I will need to add new row there (although there is an UPDATE statement in updateVoteType). The user_id will then need to be an ip address of the user if I'm right? (I allow anonymous commenting and voting). And if id field in that table is somehow set to be auto filled..

We're really sorry, but there is no way for adding like/dislike via REST API.

You can view the "voteOnComment" method in the WpdiscuzHelperAjax class, it'll help you better understand how the wpDiscuz votes are realised.