When you view a YouTube video, if the publishers of the video made it "shareable" you should be able to find a share icon underneath the video when viewed on the YouTube website. This will contain iframe information which you can just copy and paste into your survey. In your case, you also want to hide the controls, disable the keyboard controls, and autostart the video, which is found in the following example:
<iframe width="853" height="480" src="https://www.youtube.com/embed/PCdtjA32BhA?autoplay=1&controls=0&disablekb=0&rel=0
" frameborder="0" allowfullscreen></iframe>
Some browsers may not allow you to disable the keyboard controls; some will. There is probably a way to code up your own controllers. See https://developers.google.com/youtube/player_parameters
for more information.