Can i customize the widget and how?

Yes, you can customize the widget. There are two ways to do this either navigate to Settings > Follow & Subscribe or Appearance > Widgets in the WordPress Admin console. 
Image 1:Follow and Subscribe plugin settings page.

Why only Facebook and Google Plus buttons are showing? Where are the rest?

This widget shows the buttons/icons which are configured with valid URLs. Facebook and Goggle plus buttons are configured automatically by the widget so, they start showing instantly. 
Rest buttons/icons will show as soon as you fill the URLs. To fill the respective URLs move to the Configure URLs section of the plugins settings page ( image 1 ) .

Can i customize language of Facebook like, Google Plus and Twitter? 

Yes, you can customize the language from the drop-down in the Language options section of the plugin's setting page.

Why the widget is not showing on my website?

This plugin needs a active side-bar to be visible. If your theme don't have the active sidebar then, it won't show up. To make the widget working, you can manually paste the code.

For Manually positioning the Follow and Subscribe Sidebar Widget in your blog, place the below given code in the sidebar.php below div with id="secondary" or any other file as you see appropriate
 in themes folder (...\wordpress\wp-content\themes).
 <?php lafs_widget_function();?>

When I click the Like button, the popup window (or "flyout") doesn't show. Why?

If the Like button is placed near the edge of an HTML element with the overflow property set to hidden, the flyout may be clipped or completely hidden when the button is clicked. This can be remedied by setting the overflow property to a value other than hidden, such as visible, scroll, or auto.