Can I edit the CSS file to change the appearance of my website in Web Designer?

Web Designer is a WYSIWYG product and that means external CSS styles are of little to no value. The point of external styles is that you can change them e.g. to change font style or HTML colors etc. But editing external style sheets breaks the very point of a WYSIWYG designer, because then your web page is not what you see in Web Designer at all.

So while using an external style sheet is great in some circumstances, it is not applicable and adds no value to precise accurate WYSIWYG web tools.  If you want to change the font or the colors in a Web Designer website, you do it in the program, rather than playing with CSS style sheets.  There's a parallel with PDF here.  How many people do you know that hack the PDF or use text editors to edit style definitions in the actual PDF file? Of course no one does now, because the point of a PDF is that it's an exact replication of the designer's intention. Same point applies.

The aim of Web Designer is to allow you to create great looking, functional websites without the need to understand CSS, HTML or JavaScript.   Web Designer is a design-based solution, not a technical or programmer based solution.