Can I copy them word for word, and put them as the author? Do I have to link back to the original source, or can I just put the authors name?
If you are using the feeds from Google then you also need to credit them with the source url which should be an hyperlink. Also, if you notice Google doesn't include the whole of the sorry on their site, they only include the start of it or the summary and then if you click the link it will go to the news site, you should really do the same. Also don't go to the actual source of the news site and copy and paste the sorry as they pay journalists thousands per month so that they can find and write their news and some even go in dangerous places around the world to get the news.
If you don't have permission from the copyright holder then you are not allowed to copy and repost that article on any website, regardless if you give them credit and a link back. That would be a copyright violation. Even with RSS feeds this applies. Most of the news sites also explicitly disallow you from using their RSS feeds and embedding them as content in your site.
Just because you don't like an answer doesn't make it wrong and mean you should look for other opinions. Copying an article word for word is, as mentioned above, copyright violation and you need the written permission of the owner of the copyright before you can copy it. Publishing the name is not enough.