But the "B" and "C" addresses are created and appear to be OK in all ways BUT they do not appear in the Mail folder and will not send or receive as expected.
The B and C accounts are not true accounts in that they don't have their own server settings (username, password, etc.). Instead all email sent to these addresses is directed to the main account's mailbox, so when you fetch mail on your client, all mail sent to A, B or C will appear in your Inbox.
If you want to filter the B and C mail into separate folders you can setup a mail rule on your mail client to look for the 'To' address.
If you want to send mail from these addresses you need to configure your mail client to let you do so. In recent (10.11.x) versions of Mac OS X this will be configured in Mail.app for you. In other versions/apps you may have to do it yourself (add the A, B and C addresses in the 'email address' field)