Confirmation emails not being sent
I've recently had to address this issue.

1) Make sure that the PayPal's "callback" setting is enabled and set to point to your website.

2) Speak with your sysadmin and make sure that calls from PayPal are not being blocked.

3) Look in your CiviCRM logs around the time of the payment to see if there are any errors.

4) Ask your friendly neighbourhood software developer (or me or a CiviCRM partner agency if you don't have one) to add extra logging and debug output to determine if the calls are being received and traced through the system.

5) Check the spam folders - there's a lot of things that you can do if emails end up being sent to spam.

Good luck!