I see many websites that are serving news directly from yahoo and I wonder is that illegal to publish it on your own website? because I'd like to made a news site and serve only sports news.
No, it's not illegal, however you have to respect Yahoo's terms of use, which you can find here (down on the page). In short: You have to give credit to them by a link.
It isnt illegal if it is aggregated through yahoo rss and link to the news (found in the rss) is also posted with the news.