You can send emails to yourself.. I can see from the screenshot that the sender is created as a contact in CRM. Hence there should not be any issues.
If the emails remaining pending send when sent from outlook, please ensure that the E-mail access type - Outgoing value must be set as Microsoft Dynamics CRM for Outlook. Also check that On the Personal Options pane, on Email tab, and check box is checked
to "Allow Microsoft Dynamics CRM to send e-mail using Microsoft Dynamcis CRM for Outlook.
Hope it helps!
Regards, Abhishek Bakshi If you find this post helpful then please Vote as Helpful and Mark As Answer. Check my blog on https://mydynamicscrmblog.wordpress.com/