is there any CSS way to add div, p, span elements inside css content attribute? I mean code like this
.textblockquote:before{
content: "<span class='green'>“</span>";
}
you won't be able to insert other things than text-element with css
BUT, what you want to do can be achieved this way :
.textblockquote:before{
color:green; /* <-- apply the styling you want */
content: "\0022"; /* <-- escaped unicode for 'quote' */
}
In the meantime, your question has already been answered (30 months ago): Using :before and :after CSS selector to insert Html
Look : 
You can achive this with hexadecimal characters, but you shouldn't :)
See here: Adding HTML entities using CSS content
Its possible but its designed for text not html. http://www.quirksmode.org/css/content.html,
Here is an example how you can achive this in Firefox. ( 2nd answer ) Insert HTML from CSS