Is there a way I can make the videos on my website embedabble in Facebook the same way Youtube's videos are?
Youtube uses a iframe that is sized to fit the video player. Theoretically, you could do the same with your own video content.
<iframe width="X" height="Y"
Where X is width and Y is height. You might have to play with it to get it to work they way you want it to work, but this is the basic idea.