You still look to be using the Javascript button type. Moving to the Image type should fix the issue of it not displaying in Firefox. The Javascript button, from Facebook, has issues when it's being displayed within another Javascript popup like you're trying.
As for adding your own login button, all you need to do is simply add the text {JFBCLogin} wherever you want the button to appear. That will use the Javascript button, but on your home page, that shouldn't have any issues. If you'd like the code for a custom image button, we can provide that as well.
Hope that helps,
Alex