There are many reasons why this error could occur.
Before that I would recommend that you turn on your Email accounts’ Authentication (both SPF and DKIM), those are done through:
cPanel -> Authentication (under the Email section) -> Turn Off DKIM and SPF, then turn them back On
About the second issue – I believe that your domain’s mail exchanger (a setting in cPanel) is not properly configured.
If you wish to receive emails for a domain in your cPanel account you need to the following:
cPanel -> Mail Exchanger -> Select your domain -> Select Local Mail Exchanger
You should also see if your mailbox is not Suspended or Partially Suspended