Can the Menu looks/style be changed to like "Twenty Thirteen" theme?

Yes it can be changed with some CSS coding. Not seen anyone own up to having done it yet, so no code to add to a Snippet as yet.

I wouldn’t try to change the Customizr menu into the Twenty Thirteen one. A better approach is to replace it. Here are the steps:

1. Identify the php generating the menu in Twenty Thirteen and copy the code in a function in functions.php of your Customizr child theme.
2. Hook the function above to tc_menu_display() (also in functions.php). Alternatively, you may disable the output of tc_menu_display() and hook your Twenty thirteen menu function to some other Customizr hook, depending on where you want the menu to appear.
3. Identify and copy all the CSS for the menu from Twenty Thirteen into style.css of your Customizr child theme.

is there any simpler way to do it? like adding code snippet in custom code box or any pluggin?

@acub, referring to Hooks is a bit daunting to non-Developers. @nikeo did publish this Snippet to help.

You’re right, rdell, but Customizr automatically adds bootstrap classes and properties to the menu and one should keep in mind that overriding bootstrap menu is no easy task either. Besides classes it also uses javascript and makes use of specific non-standard properties, like data-toggle and data-target.

From where I see it, hooking the menu generating function and adding the necessary CSS to Customizr (being copy/paste) looks less daunting than turning bootstrap 2.3.2 menu into 20_13 through CSS alone.