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You can embed the video very easily, and the 'slow down' compared to having the video on-site, is minimal.
You could contact the person who placed the vids on YouTube and ask them - but embedding is probably a much slicker solution.
Uploading the file to your website would almost certainly be a violations of YouTube's terms of service, and a violation of the rights of both the maker of the video and YouTube.
That you are unable to contact the author does not invalidate a copyright! (Note that there is a move to update the copyright laws to more fairly deal with abandoned copyrights, but as I understand it there is no relief under currently law.)