Is there a way so that when users set up an account their folder structure includes a /domains folder with their first domain in it? Then each add-on domain creates another entry in there. I find the cPanel directory structure to be rather messy compared to DirectAdmin.

Also is there a way to change the yourdomain.com/cpanel on customer's accounts to something else?

You probably need to contact Cpanel support itself to get answer of these queries.

But I will still suggest you not to play with Cpanel default directory structure

I think you can do custom bash script using cpanel's pre and post account creation script. I really don't remember the file name now, but you can just contact cpanel.net to ask about this.