Akashmitra,
I'm not sure if you've installed JLinked yet, but in that package is an updated login module, SCLogin. That works with both JFBConnect and JLinked, and is going to be included in the next release of JFBConnect (replacing the JFBCLogin module).
First, I'd recommend you use that module instead. In the tmpl folder of SCLogin, there's a login.php and logout.php file, making customizations much simpler and the code has been made much cleaner.
You're free to add your own CSS attributes to your template or creating a template override, where you can modify the layout of the template completely. To create a template override, simply copy /modules/mod_sclogin/tmpl/login.php to /templates/<YOUR_TEMPLATE>/html/mod_sclogin/login.php (creating that directory structure if necessary) and modifying the file there. That prevents any updates to the SCLogin module from overwriting your template changes.
Hope that helps,
Alex