If you want the blue box to extend to the sides of the page, please create a new section with a row and one column in it. Add a solid blue background in the section and then insert the quote element in the column on that section.
And by the way, only the quote element has the option to edit/create a closing and opening quotes. There aren't any other element that does that. With your custom JS and the quote element, you might be able to have a rotating quotation. Regretfully this that requires custom development, it is beyond the scope of our support.
Thank you for your understanding.