Is there easy way to parse a HTML page to find all the fonts used (or all the font stacks used)?
Or similarly, is there a script that parses a page and returns which
For your first question you can use a specialized website like https://unused-css.com. Sometimes the css file generated causes problems. The advantage of this tool is that it can crawl all site pages to an overall summary. It will be difficult to achieve with an browser extension (although possible).
An alternative solution for a developer is a browser extension : Firefox extensions: Dustme selector or Css usage
Chrome extensions: Unused CSS or Css remove and combine
Best solution for an experienced developer : Install a free tool from github : https://github.com/search?utf8=%E2%9C%93&q=unused+css
For your second question, no online tool existed to extract all font from a webpage. I created my own tool :
http://website-font-analyzer.com/
This tool can detect all fonts from an url and also detect which websites use a font.