If I send someone a PowerPoint, do they get the videos in it, too?

Well, it all depends on whether you have embeded the video into the powerpoint file or just linked it. And the difference between the two is as following:

What is Hyperlinking?

Hyperlinking is an element in an electronic document that links to another place. Typically, you click on the hyperlink to follow the link or path. When you hyperlink to a video, you are creating a path or “directions,” to the video and the video player application.

What is Embedding?

Inserting the downloaded video within the application so it plays in the frame/slide of the application.

And for safety's sake, when you email a powerpoint file, I suggest you to convert the file into a flash. Then all the hyperlinked files would be converted to be a part of the flash. And you don't need to worry if the file has been sent completely.

To convert powerpoint into flash, you can try the software here http://www.sameshow.com/ppt2flash/samples.html

No, it's like when you get a powerpoint from someone with a soundfile and you try to play it and it doesn't work, same with videos. You have to have the video present on the harddirve. The video clip in powerpoint is kind of like a shortcut, but plays in the app

No. The video is usually linked to the PPT. When you send it to others, you need to send the video too and put them in the same folder on the local drive after receiving them.