Yes its usually free and available for all kinda use . Do read their license if there is any . Usually the feeds that they want you not to use for commercial purposes are not free . For Example BBC . But make sure you shouldn’t plagiarize and give due credit to the news agency .
A good example is Google news . They just gather news from all the different feeds and present it in a better way . Similarly there are many services which provide APIs so you can easily consume their feeds i.e. Twitter .
If you want to you can mix and match RSS into feedburner and use it wherever. Yahoo used to have this tool called Yahoo Pipes (or something) where you could put in filters on what you wanted to use and what you didn’t. Don’t know if it still exists. Anyone else play with that?