Order confirmation emails and others are not coming through.
AbanteCart will try to use local SMTP/PHP mail to send the emails out. If you don’t have that working on the hosting/server where your website is on, then you have to discuss this with the server administrators (hosting support) and locate the problem there. It might be that the way emails are structured inside AbanteCart, they get refused by the server and not sent.
Try different email domain for testing (gmail, yahoo etc) to make sure this is not a receiver issue (letter is rejected as spam so it could be either put into the "Spam" mail section or simply blocked, recipient's mailbox is full etc).
Check AbanteCart error log (Admin > System > Logs > Error log) for mail related errors and warnings.
Check your servers mail log if possible. This will at minimum show you if an email was sent out from the server. Typically this is found at /var/log/maillog but it is dependant on your server's OS and mail software.