I'm not exactly sure of the file you'd need to edit for the AJAX Login module. Usually, the file would be something like /modules/mod_improved_ajax_login/tmpl/default.php, though there may be different template files other than default.php file in that directory. Once you find the right file, the best thing to do is create a template override of that file by copying it to /templates/<YOUR_TEMPLATE>/html/mod_improved_ajax_login/<file>.php (creating any directories that aren't already there along the way. A template override will make sure that your changes 'stick' even if you update the module in the future.
Then, edit that file to add in JFBConnect's Login with Facebook button. To do that, I'd honestly recommend you just take a screen capture of the button that's already there and use that for a new image button. You can add that with the following HTML:
<a href="javascript:void(0)" onclick="jfbc.login.login_custom();"><img src="/linktoimage.jpg" /></a>
You can see more information about custom buttons in our
Facebook for Joomla Common Support Questions
guide.
Finally, for the "Edit" page, can you tell me what extension is creating that page? Is that Joomla, JomSocial, or something else? A good way to narrow down the template file to edit is to disable SEF, temporarily, and look at the raw URL. That usually gives great hints of what file needs to be edited.
Hope that helps, but let us know if you need anything more!
Thanks,
Alex