No, you may not download, reproduce, or screenshare YouTube videos. When using YouTube you are subject to their terms of service, which specify that you are not allowed to download or redistribute their content. The Permissions and Restrictions section of their terms of service states1, "The following restrictions apply to your use of the Service. You are not allowed to:
1. access, reproduce, download, distribute, transmit, broadcast, display, sell, license, alter, modify or otherwise use any part of the Service or any Content except: (a) as expressly authorized by the Service; or (b) with prior written permission from YouTube and, if applicable, the respective rights holders;
2. circumvent, disable, fraudulently engage with, or otherwise interfere with any part of the Service (or attempt to do any of these things), including security-related features or features that (a) prevent or restrict the copying or other use of Content or (b) limit the use of the Service or Content;"
If you want to reuse YouTube videos we recommend that you reach out to the rights holder to ask for permission and for access to a copy you can use.
For more information on linking to online video, see FAQ 0.7, Can I embed or link to free online video services (ex. YouTube, Vimeo) content in LEARN?
For more information on how to ask permission, see FAQ 1.11 How do I get permission to use someone else’s work?
1This quote was copied for this FAQ answer in September 2020, and is subject to change. Review the YouTube Terms of Service directly for more current information.
