Is YouTube videos legal

Yes, it is. The easy way to do it is (when you're in YouTube, playing the video you want to link to) click on "embed" and add the code to your website.

Or, just to provide a link, copy the url that's displayed in your browser window.

However, if the link is to copyrighted content, you could get in trouble for linking to it. The argument that you didn't post the content will not keep you out of jail. There are plenty of video links sites that have been closed by the government, even though they contained no actual copyrighted content.