Can I clone WP to another directory on the same server?

Yes you can clone the website on the same server in another directory . You may follow below steps.

1. Copy entire wordpress root directory in another folder for ex. Beta.
2. Create a new DB and copy the existing database into the new DB . You can use same DB by changing WP prefix but I would recommend having a new DB.
3. Change the db details in wp-config.php files.

If you have any doubts in above please let me know . I will guide you for the same

I would recommend to clone it on a subdomain. Something like "testing.myfriendswp.com". I have tried this approach and it works fine. If you have a cpanel, you will see an option to create a subdomain in it. create a subdomain and point it to a folder inside public_html. So, for example, your subdomain "testing.myfriendswp.com" will be pointed to a directory "public_html/testing". Once you have the subdomain created:

1. copy the WP files from the main domain to subdomain
2. create a new database and import tables from the main DB to it.
3. set appropriate DB credentials in wp-config.php file
4. change the domain name in the wp-options table in the new DB.
5. boot up WP on the subdomain and refresh the permalink settings.
6. Run a search replace script on DB to replace main domain to the subdomain.

For extra security, add a robots.txt file on your subdomain to prevent the instance from being crawled by Search Engine Robots.

Thanks