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No, because that requires the ability to crawl your entire site. Due to PHP and host restrictions, as well as Joomla!'s ability to create infinitely nested structures, this can not work reliably. Your best bet is using a commercial link scanner software application, running on your PC, which will crawl your site and after a few hours will produce a report of all the broken links and the links on which they appear.

I don;t think so. If someone found a way to automatically fix broken links I guess he would own the Internet overnight :D "Fixing" a broken link is something manual. You have to figure out why you have a broken link and act accordingly. For example, it could be a missing file (replace the file or remove the reference), a moved resource (update the reference), a problem with the server setup (fix the server setup) and so on and so on. It's such a broad and fuzzy topic that makes automated tools impractical. Automated tools are good for simple tasks which have to be repeated numerous times or for huge lists of relatively simple tasks. This is where computers excel at. Anything which requires fuzzy logic is much better performed by human with incredibly enhanced precision and accuracy.

So, my advice is using a tool to identify broken links and your brain to figure out how to fix them. I know it's not very fun, but it's the most efficient way.