Four years of applying for Yahoo's free, nonprofit listing so far for me, and no success yet. My site is absolutely noncommercial. No ads, nothing remotely financial. And the site has good content and lots of visitors. But Yahoo has consistently declined my applications for the free listing that they offer.
depends on the industry. If it's a competitive category then it could take forever. If it's more of a niche category could happen straight away.... nobody knows for sure because it all depends on individual websites and how they fit in with the category
Yahoo is about money. You will be waiting till the end of time and never get a free listing in their directory.