I know Google is giving a penalties for websites with duplicate content. What happens if I'm having an RSS feed with news articles and other sites publishes on their website my news? Isn't it duplicate content?
It is duplicate content but they are the ones who will be hit with duplicate content penalties and issues as they are the ones republishing your work.
Google has recently made improvements to their algorithm to deal with this and ensure that the original publisher gets credit for the work but it still isn't perfect. However, you can help yo mitigate this by publish a hard link to the original article in your RSS feed so if someone is auto-publishing your articles from that feed that link will show that you are the original author.
I think the duplicate content issue relates to content being taken from your site without permission. As you've given permission I don't think there should be any issues for either site as long as they are publishing a link back to your site. It's also best to just publish a teaser in the feed so they are only displaying a summary and people need to navigate back to your site for the rest. That should actually improve your ranking instead of the other way around.