Is there a way to add a youtube video to a personal Photo page? I thought one of my classmates had a video of one of his trips in with his personal Photos, or at least a link to one.

Your member can capture the embed code from YouTube and paste it into one of their boxes in their profile. When they save it, it will appear as a video.

See example

Got it. Thank you very much. I knew there was a way but forgot the boxes on the Profile Page. Now, my next project is to change the font and enlarge the size of this print. Oops, the size and font change when I click on save, so problem solved.

Got another question. Recently, I did a Tandem Skydive and it was captured on video, and the Skydiving company set it to music. Then when I copied it to Youtube, they eliminated the music and speach, apparently concerned that some of the music may have a copyright. I don't really care about the music, but would like my classmates to have the opportunity to hear what I was saying. I have a copy of the video. Is there a way that I can save it to some location and provide them with a link to it so they could hear the verbal part of the video?

I have found if you add a disclaimer stating something along the lines of "no copyright infringement is intended, as per Youtube guidelines", that Youtube tends to allow the music in the video. This has been working for several users of this video uploading service. So perhaps if you were to: delete your entire video, then upload the video (with the music and natural sound mixed in together again) and then type in the previously mentioned disclaimer, Youtube officials will read this statement and allow the audio and not remove it from the video, as you have described. It is a case by case basis but I have noticed Youtube will often OK it if you follow these steps. (It has worked for me.)
You can also change the listing / setting of the video from public to unlisted or private. Doing this will also enable the video linking you are interesting in using and the disclaimer I've mentioned should help with the audio deletion / muting situation.
Hope it helps.

Thank you. I will give it a try and get back to you.