Since you're not cloning the button itself, but a parent, you need to do a deep clone:
this.fileTemplate = $('.file:first').clone(true,true);
$('.file:first').remove();
http://api.jquery.com/clone/#clone-withDataAndEvents-deepWithDataAndEvents
However, if you're removing the element anyway, you don't need to clone it at all -- just store the div with all of its events by using .detach() instead of .remove():
this.fileTemplate = $('.file:first').detach();
http://api.jquery.com/detach/
To add copies of that element, deep-clone it after it's detached:
clone_copy = this.fileTemplate.clone(true,true);
clone_copy.appendTo('#container');