it depends on the license the video was uploaded with. If it was uploaded with the standard license then No, you cannot use it without permission. If it was uploaded using the creative commons license then yes you can. As for the video that you uploaded, its kind of a gray area. Its under standard, but they include the download link. You can try and use it, and then if it gets taken down youll know your answer. I wouldnt use it because, you dont have proof that the person sharing that song has the rights to that song.