Is it legal to download YouTube videos which are licensed under Standard YouTube license?
If so, is it legal to edit a downloaded video and use it to make another video?
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Sign up to join this communityThis is in violation of YouTubes terms of service and therefore is Copyright violation unless you have the permission of the author(s) (which you say you don't) or it constitutes fair use (which it almost certainly doesn't). As part of the footage involves a logo and images of a MotoGP, it is probably also trademark violation too.
Let's say A uploads a video, which B finds interesting. Now, B wants to use a part of that video for his own video, and does so without the knowledge of A. This would be a definite copyright violation since A owns the copyright to the video he uploaded. To avoid this, B must first get permission from A to reproduce part of his video and only then can he do so.