Hey there,
I am really sorry for the delay of this reply as it is a weekend for us here.
This is the file output that Easysocial toolbar and that login icon as well.
JoomlaFolder/components/com_easysocial/themes/wireframe/toolbar/default.php , you can template override this file into your current template file directory
JoomlaFolder/templates/YourCurrentTemplate/html/com_easysocial/toolbar/default.php , for those new folder you have to manually create it.
In this method, you do not need to replace the code again when you update to next release version.
Also is there a way to hide the whole Login Layout (or) REPLACE/hide the login FORM and register buttons? what file can I modify? I expected this form to show the JFBconnect's SClogin form after integration.
When you enabled this Jfbconnect integration setting from Easysocial, it will show this social button under the login form, I've help you enabled a few setting from Easysocial backend, it should display correctly now.
Backend > Easysocial > setting > users > registration > Allow New User Registrations - YES
Backend > Easysocial > setting > social > Facebook > Allow Registrations - YES
Backend > Easysocial > setting > social > Facebook > Use JFBConnect Buttons - YES