Hi,
Easy Profile extends Joomla user management (not replace), registration/edit profile pages are the same of Joomla. Custom fields are loaded by our user plugin and tabs are generated by javascript.

Submit and Cancel buttons in edit profile page comes from Joomla and not from Easy Profile.

What is the css selector for each of the buttons so I can properly style them for my template?

this depends on your template, many template overrides Joomla edit profile page. Joomla (3.4.8) default classes are:
- Submit button: btn btn-primary
- Cancel button: btn

Thanks, the final selector for the Submit button that I got to work was .btn.btn-primary.validate which might help others looking to find the selector for styling this button.

You pointed me in the right direction, little sleuthing and presto, button styled perfectly.
We can say this is "accpeted"
Your help was much appreciated, keep up the good work on the component, it's very useful and continuing to develop it will solve a lot of headaches for developers.
Thank you!