You can use sites like y2mate.com to download youtube videos and then upload them here. There is either a 100MB or 150MB upload limit, so choose a resolution that will let you upload the archived video. If you're a computer toucher, you can figure out how to use command line programs like youtube-dl to download from lots of sites and programs like ffmpeg for encoding videos in better quality at lower file sizes. There are gui programs that use ffmpeg like Handbrake. A ghetto way to record livestreams is by using VLC player to watch a network stream and hitting the record button. Screenshot videos using the print screen button and then paste them into Paint, GIMP, Photoshop, etc then crop them and post them. You can also use browser addons like Fireshot to screencap entire webpages and use archive.md to archive websites. Don't use archive.org because they will purge archives.
There is usually a semi-active thread about archiving in General and sometimes in cow/community specific subforums for cows who are known to delete things.