Just want to know if it\'s possible to have a div tag inside the head element?
No, Also, there is no difference between using tag, since the tag is only meant to be for metadata (such as title and page description), scripts, styles, and other stuff which isn't meant to be displayed. Although putting it in the works, it's horrible to do so, and you shouldn't put it there (and the specification says that doing that is not valid HTML. Thanks @t.niese); it's invalid HTML
" or ' for attribute values (such as id in your case), it's just what you prefer. And yes, using ' is completely valid. I like doing that, since I don't have to hold shift, but it's completely up to you.